How to localize ASP.NET Identity UserName and Password error messages?

For ASP.NET Core: (Microsoft.AspNetCore.Identity 1.0.0)

Create a class that inherits IdentityErrorDescriber and override the desired error messages.

public class CustomIdentityErrorDescriber : IdentityErrorDescriber
{
    public override IdentityError DefaultError() { return new IdentityError { Code = nameof(DefaultError), Description = $"An unknown failure has occurred." }; }
    public override IdentityError ConcurrencyFailure() { return new IdentityError { Code = nameof(ConcurrencyFailure), Description = "Optimistic concurrency failure, object has been modified." }; }
    public override IdentityError PasswordMismatch() { return new IdentityError { Code = nameof(PasswordMismatch), Description = "Incorrect password." }; }
    public override IdentityError InvalidToken() { return new IdentityError { Code = nameof(InvalidToken), Description = "Invalid token." }; }
    public override IdentityError LoginAlreadyAssociated() { return new IdentityError { Code = nameof(LoginAlreadyAssociated), Description = "A user with this login already exists." }; }
    public override IdentityError InvalidUserName(string userName) { return new IdentityError { Code = nameof(InvalidUserName), Description = $"User name '{userName}' is invalid, can only contain letters or digits." }; }
    public override IdentityError InvalidEmail(string email) { return new IdentityError { Code = nameof(InvalidEmail), Description = $"Email '{email}' is invalid."  }; }
    public override IdentityError DuplicateUserName(string userName) { return new IdentityError { Code = nameof(DuplicateUserName), Description = $"User Name '{userName}' is already taken."  }; }
    public override IdentityError DuplicateEmail(string email) { return new IdentityError { Code = nameof(DuplicateEmail), Description = $"Email '{email}' is already taken."  }; }
    public override IdentityError InvalidRoleName(string role) { return new IdentityError { Code = nameof(InvalidRoleName), Description = $"Role name '{role}' is invalid."  }; }
    public override IdentityError DuplicateRoleName(string role) { return new IdentityError { Code = nameof(DuplicateRoleName), Description = $"Role name '{role}' is already taken."  }; }
    public override IdentityError UserAlreadyHasPassword() { return new IdentityError { Code = nameof(UserAlreadyHasPassword), Description = "User already has a password set." }; }
    public override IdentityError UserLockoutNotEnabled() { return new IdentityError { Code = nameof(UserLockoutNotEnabled), Description = "Lockout is not enabled for this user." }; }
    public override IdentityError UserAlreadyInRole(string role) { return new IdentityError { Code = nameof(UserAlreadyInRole), Description = $"User already in role '{role}'."  }; }
    public override IdentityError UserNotInRole(string role) { return new IdentityError { Code = nameof(UserNotInRole), Description = $"User is not in role '{role}'."  }; }
    public override IdentityError PasswordTooShort(int length) { return new IdentityError { Code = nameof(PasswordTooShort), Description = $"Passwords must be at least {length} characters."  }; }
    public override IdentityError PasswordRequiresNonAlphanumeric() { return new IdentityError { Code = nameof(PasswordRequiresNonAlphanumeric), Description = "Passwords must have at least one non alphanumeric character." }; }
    public override IdentityError PasswordRequiresDigit() { return new IdentityError { Code = nameof(PasswordRequiresDigit), Description = "Passwords must have at least one digit ('0'-'9')." }; }
    public override IdentityError PasswordRequiresLower() { return new IdentityError { Code = nameof(PasswordRequiresLower), Description = "Passwords must have at least one lowercase ('a'-'z')." }; }
    public override IdentityError PasswordRequiresUpper() { return new IdentityError { Code = nameof(PasswordRequiresUpper), Description = "Passwords must have at least one uppercase ('A'-'Z')." }; }
}

On your Startup class, register the custom ErrorDescriber inside ConfigureServices:

services.AddIdentity<ApplicationUser, IdentityRole>()
                .AddErrorDescriber<CustomIdentityErrorDescriber>(); // Add this line

UPDATE: Below you can find already translated versions for spanish and portuguese. Double check them!

public class SpanishIdentityErrorDescriber : IdentityErrorDescriber
{
    public override IdentityError DefaultError() { return new IdentityError { Code = nameof(DefaultError), Description = $"Ha ocurrido un error." }; }
    public override IdentityError ConcurrencyFailure() { return new IdentityError { Code = nameof(ConcurrencyFailure), Description = "Ha ocurrido un error, el objeto ya ha sido modificado (Optimistic concurrency failure)." }; }
    public override IdentityError PasswordMismatch() { return new IdentityError { Code = nameof(PasswordMismatch), Description = "Password Incorrecta." }; }
    public override IdentityError InvalidToken() { return new IdentityError { Code = nameof(InvalidToken), Description = "Ha ingresado un código Inválido." }; }
    public override IdentityError LoginAlreadyAssociated() { return new IdentityError { Code = nameof(LoginAlreadyAssociated), Description = "Un usuario con ese nombre ya existe." }; }
    public override IdentityError InvalidUserName(string userName) { return new IdentityError { Code = nameof(InvalidUserName), Description = $"El nombre de usuario '{userName}' es inválido. Solo puede contener letras y números." }; }
    public override IdentityError InvalidEmail(string email) { return new IdentityError { Code = nameof(InvalidEmail), Description = $"La dirección de email '{email}' es incorrecta."  }; }
    public override IdentityError DuplicateUserName(string userName) { return new IdentityError { Code = nameof(DuplicateUserName), Description = $"El usuario '{userName}' ya existe, por favor ingrese un nombre diferente."  }; }
    public override IdentityError DuplicateEmail(string email) { return new IdentityError { Code = nameof(DuplicateEmail), Description = $"La direccion de email '{email}' ya se encuentra registrada. Puede recupar su contraseña para ingresar nuevamente al sistema."  }; }
    public override IdentityError InvalidRoleName(string role) { return new IdentityError { Code = nameof(InvalidRoleName), Description = $"El nombre de rol '{role}' es inválido."  }; }
    public override IdentityError DuplicateRoleName(string role) { return new IdentityError { Code = nameof(DuplicateRoleName), Description = $"El nombre de rol '{role}' ya existe."  }; }
    public override IdentityError UserAlreadyHasPassword() { return new IdentityError { Code = nameof(UserAlreadyHasPassword), Description = "El usuario ya tiene contraseña." }; }
    public override IdentityError UserLockoutNotEnabled() { return new IdentityError { Code = nameof(UserLockoutNotEnabled), Description = "El bloqueo no esta habilitado para este usuario." }; }
    public override IdentityError UserAlreadyInRole(string role) { return new IdentityError { Code = nameof(UserAlreadyInRole), Description = $"El usuario ya es parte del rol '{role}'."  }; }
    public override IdentityError UserNotInRole(string role) { return new IdentityError { Code = nameof(UserNotInRole), Description = $"El usuario no es parte del rol '{role}'."  }; }
    public override IdentityError PasswordTooShort(int length) { return new IdentityError { Code = nameof(PasswordTooShort), Description = $"La contraseña deben tener un largo mínimo de {length} caracteres."  }; }
    public override IdentityError PasswordRequiresNonAlphanumeric() { return new IdentityError { Code = nameof(PasswordRequiresNonAlphanumeric), Description = "La contraseña debe contener al menos un caracter alfanumérico." }; }
    public override IdentityError PasswordRequiresDigit() { return new IdentityError { Code = nameof(PasswordRequiresDigit), Description = "La contraseña debe incluir al menos un dígito ('0'-'9')." }; }
    public override IdentityError PasswordRequiresLower() { return new IdentityError { Code = nameof(PasswordRequiresLower), Description = "La contraseña debe incluir al menos una letra minúscula ('a'-'z')." }; }
    public override IdentityError PasswordRequiresUpper() { return new IdentityError { Code = nameof(PasswordRequiresUpper), Description = "La contraseña debe incluir al menos una letra MAYÚSCULA ('A'-'Z')." }; }
}

Portuguese: (many thanks to furlanrapha)

public class PortugueseIdentityErrorDescriber : IdentityErrorDescriber
{
    public override IdentityError DefaultError() { return new IdentityError { Code = nameof(DefaultError), Description = $"Um erro desconhecido ocorreu." }; }
    public override IdentityError ConcurrencyFailure() { return new IdentityError { Code = nameof(ConcurrencyFailure), Description = "Falha de concorrência otimista, o objeto foi modificado." }; }
    public override IdentityError PasswordMismatch() { return new IdentityError { Code = nameof(PasswordMismatch), Description = "Senha incorreta." }; }
    public override IdentityError InvalidToken() { return new IdentityError { Code = nameof(InvalidToken), Description = "Token inválido." }; }
    public override IdentityError LoginAlreadyAssociated() { return new IdentityError { Code = nameof(LoginAlreadyAssociated), Description = "Já existe um usuário com este login." }; }
    public override IdentityError InvalidUserName(string userName) { return new IdentityError { Code = nameof(InvalidUserName), Description = $"Login '{userName}' é inválido, pode conter apenas letras ou dígitos." }; }
    public override IdentityError InvalidEmail(string email) { return new IdentityError { Code = nameof(InvalidEmail), Description = $"Email '{email}' é inválido." }; }
    public override IdentityError DuplicateUserName(string userName) { return new IdentityError { Code = nameof(DuplicateUserName), Description = $"Login '{userName}' já está sendo utilizado." }; }
    public override IdentityError DuplicateEmail(string email) { return new IdentityError { Code = nameof(DuplicateEmail), Description = $"Email '{email}' já está sendo utilizado." }; }
    public override IdentityError InvalidRoleName(string role) { return new IdentityError { Code = nameof(InvalidRoleName), Description = $"A permissão '{role}' é inválida." }; }
    public override IdentityError DuplicateRoleName(string role) { return new IdentityError { Code = nameof(DuplicateRoleName), Description = $"A permissão '{role}' já está sendo utilizada." }; }
    public override IdentityError UserAlreadyHasPassword() { return new IdentityError { Code = nameof(UserAlreadyHasPassword), Description = "Usuário já possui uma senha definida." }; }
    public override IdentityError UserLockoutNotEnabled() { return new IdentityError { Code = nameof(UserLockoutNotEnabled), Description = "Lockout não está habilitado para este usuário." }; }
    public override IdentityError UserAlreadyInRole(string role) { return new IdentityError { Code = nameof(UserAlreadyInRole), Description = $"Usuário já possui a permissão '{role}'." }; }
    public override IdentityError UserNotInRole(string role) { return new IdentityError { Code = nameof(UserNotInRole), Description = $"Usuário não tem a permissão '{role}'." }; }
    public override IdentityError PasswordTooShort(int length) { return new IdentityError { Code = nameof(PasswordTooShort), Description = $"Senhas devem conter ao menos {length} caracteres." }; }
    public override IdentityError PasswordRequiresNonAlphanumeric() { return new IdentityError { Code = nameof(PasswordRequiresNonAlphanumeric), Description = "Senhas devem conter ao menos um caracter não alfanumérico." }; }
    public override IdentityError PasswordRequiresDigit() { return new IdentityError { Code = nameof(PasswordRequiresDigit), Description = "Senhas devem conter ao menos um digito ('0'-'9')." }; }
    public override IdentityError PasswordRequiresLower() { return new IdentityError { Code = nameof(PasswordRequiresLower), Description = "Senhas devem conter ao menos um caracter em caixa baixa ('a'-'z')." }; }
    public override IdentityError PasswordRequiresUpper() { return new IdentityError { Code = nameof(PasswordRequiresUpper), Description = "Senhas devem conter ao menos um caracter em caixa alta ('A'-'Z')." }; }
}

As of version 2 of identity which released on 20 march 2014 you can now have localized error messages.

First install the identity localized package.

Install-Package Microsoft.AspNet.Identity.Core.fr

Then the proper culture must be set in order to get localized messages for example one way to set culture is in web.config

<system.web>
      <globalization culture="fr-FR" uiCulture="fr"/>
</system.web>

ASP NET Core workaround (25.11.2016)

You can inject IStringLocalizer into custom IdentityErrorDescriber

1) Create custom IdentityErrorDescriber (see Gerardo Grignoli answer)

public class MultilanguageIdentityErrorDescriber : IdentityErrorDescriber
{
    private readonly IStringLocalizer<SharedResource> _localizer;

    public MultilanguageIdentityErrorDescriber(IStringLocalizer<SharedResource> localizer)
    {
        _localizer = localizer;
    }

    public override IdentityError DuplicateEmail(string email)
    {
        return new IdentityError()
        {
            Code = nameof(DuplicateEmail),
            Description = string.Format(_localizer["Email {0} is already taken."], email)
        };
    }

    // DuplicateUserName, InvalidEmail, DuplicateUserName etc
}

2) Register MultilanguageIdentityErrorDescriber in Startup.cs

services.AddIdentity<IdentityUser, IdentityRole>()
            .AddErrorDescriber<MultilanguageIdentityErrorDescriber>()
            .AddDefaultTokenProviders();

3) Add error messages to SharedResource.language.resx.

this is for dear Farsi(Persian) speakers

using Microsoft.AspNetCore.Identity;

namespace WebApplication.Admin.Helpers
{
    public class CustomIdentityErrorDescriber : IdentityErrorDescriber
    {
        public override IdentityError DefaultError() { return new IdentityError { Code = nameof(DefaultError), Description = $"یک خطای ناشناخته رخ داده است." }; }
        public override IdentityError ConcurrencyFailure() { return new IdentityError { Code = nameof(ConcurrencyFailure), Description = "رکورد جاری پیشتر ویرایش شده‌است و تغییرات شما آن‌را بازنویسی خواهد کرد." }; }
        public override IdentityError PasswordMismatch() { return new IdentityError { Code = nameof(PasswordMismatch), Description = "کلمه عبور نادرست است." }; }
        public override IdentityError InvalidToken() { return new IdentityError { Code = nameof(InvalidToken), Description = "کلمه عبور نامعتبر است." }; }
        public override IdentityError LoginAlreadyAssociated() { return new IdentityError { Code = nameof(LoginAlreadyAssociated), Description = "این کاربر قبلأ اضافه شده‌است." }; }
        public override IdentityError InvalidUserName(string userName) { return new IdentityError { Code = nameof(InvalidUserName), Description = $"نام کاربری '{userName}' نامعتبر است، فقط می تواند حاوی حروف ویا اعداد باشد." }; }
        public override IdentityError InvalidEmail(string email) { return new IdentityError { Code = nameof(InvalidEmail), Description = $"ایمیل '{email}' نامعتبر است." }; }
        public override IdentityError DuplicateUserName(string userName) { return new IdentityError { Code = nameof(DuplicateUserName), Description = $"این نام کاربری '{userName}' به کاربر دیگری اختصاص یافته است." }; }
        public override IdentityError DuplicateEmail(string email) { return new IdentityError { Code = nameof(DuplicateEmail), Description = $"ایمیل '{email}' به کاربر دیگری اختصاص یافته است." }; }
        public override IdentityError InvalidRoleName(string role) { return new IdentityError { Code = nameof(InvalidRoleName), Description = $"نام نقش '{role}' نامعتبر است." }; }
        public override IdentityError DuplicateRoleName(string role) { return new IdentityError { Code = nameof(DuplicateRoleName), Description = $"این نام نقش '{role}' به کاربر دیگری اختصاص یافته است." }; }
        public override IdentityError UserAlreadyHasPassword() { return new IdentityError { Code = nameof(UserAlreadyHasPassword), Description = "کلمه‌ی عبور کاربر قبلأ تنظیم شده‌است." }; }
        public override IdentityError UserLockoutNotEnabled() { return new IdentityError { Code = nameof(UserLockoutNotEnabled), Description = "این کاربر فعال است." }; }
        public override IdentityError UserAlreadyInRole(string role) { return new IdentityError { Code = nameof(UserAlreadyInRole), Description = $"این نقش '{role}' قبلأ به این کاربر اختصاص یافته است." }; }
        public override IdentityError UserNotInRole(string role) { return new IdentityError { Code = nameof(UserNotInRole), Description = $"این نقش '{role}' قبلأ به این کاربر اختصاص نیافته است." }; }
        public override IdentityError PasswordTooShort(int length) { return new IdentityError { Code = nameof(PasswordTooShort), Description = $"کلمه عبور باید حداقل {length} کاراکتر باشد." }; }
        public override IdentityError PasswordRequiresNonAlphanumeric() { return new IdentityError { Code = nameof(PasswordRequiresNonAlphanumeric), Description = "کلمه عبور باید حداقل یک کاراکتر غیر از حروف الفبا داشته باشد." }; }
        public override IdentityError PasswordRequiresDigit() { return new IdentityError { Code = nameof(PasswordRequiresDigit), Description = "کلمه عبور باید حداقل یک عدد داشته باشد." }; }
        public override IdentityError PasswordRequiresLower() { return new IdentityError { Code = nameof(PasswordRequiresLower), Description = "کلمه عبور باید حداقل یک حرف کوچک داشته باشد." }; }
        public override IdentityError PasswordRequiresUpper() { return new IdentityError { Code = nameof(PasswordRequiresUpper), Description = "کلمه عبور باید حداقل یک حرف بزرگ داشته باشد." }; }
        public override IdentityError RecoveryCodeRedemptionFailed() { return new IdentityError { Code = nameof(RecoveryCodeRedemptionFailed), Description = "بازیابی ناموفق بود." }; }
        public override IdentityError PasswordRequiresUniqueChars(int uniqueChars) { return new IdentityError { Code = nameof(PasswordRequiresUniqueChars), Description = $"کلمه عبور باید حداقل داراى {uniqueChars} حرف متفاوت باشد." }; }
    }
}