How do I change this query so it returns all u.usergroups?

from u in usergroups
from p in u.UsergroupPrices
select new UsergroupPricesList
{
UsergroupID = u.UsergroupID,
UsergroupName = u.UsergroupName,
Price = p.Price
};

adapted from MSDN, how to left join using EF 4

var query = from u in usergroups
            join p in UsergroupPrices on u.UsergroupID equals p.UsergroupID into gj
            from x in gj.DefaultIfEmpty()
            select new { 
                UsergroupID = u.UsergroupID,
                UsergroupName = u.UsergroupName,
                Price = (x == null ? String.Empty : x.Price) 
            };

It might be a bit of an overkill, but I wrote an extension method, so you can do a LeftJoin using the Join syntax (at least in method call notation):

persons.LeftJoin(
    phoneNumbers,
    person => person.Id,
    phoneNumber => phoneNumber.PersonId,
    (person, phoneNumber) => new
        {
            Person = person,
            PhoneNumber = phoneNumber?.Number
        }
);

My code does nothing more than adding a GroupJoin and a SelectMany call to the current expression tree. Nevertheless, it looks pretty complicated because I have to build the expressions myself and modify the expression tree specified by the user in the resultSelector parameter to keep the whole tree translatable by LINQ-to-Entities.

public static class LeftJoinExtension
{
    public static IQueryable<TResult> LeftJoin<TOuter, TInner, TKey, TResult>(
        this IQueryable<TOuter> outer,
        IQueryable<TInner> inner,
        Expression<Func<TOuter, TKey>> outerKeySelector,
        Expression<Func<TInner, TKey>> innerKeySelector,
        Expression<Func<TOuter, TInner, TResult>> resultSelector)
    {
        MethodInfo groupJoin = typeof (Queryable).GetMethods()
                                                 .Single(m => m.ToString() == "System.Linq.IQueryable`1[TResult] GroupJoin[TOuter,TInner,TKey,TResult](System.Linq.IQueryable`1[TOuter], System.Collections.Generic.IEnumerable`1[TInner], System.Linq.Expressions.Expression`1[System.Func`2[TOuter,TKey]], System.Linq.Expressions.Expression`1[System.Func`2[TInner,TKey]], System.Linq.Expressions.Expression`1[System.Func`3[TOuter,System.Collections.Generic.IEnumerable`1[TInner],TResult]])")
                                                 .MakeGenericMethod(typeof (TOuter), typeof (TInner), typeof (TKey), typeof (LeftJoinIntermediate<TOuter, TInner>));
        MethodInfo selectMany = typeof (Queryable).GetMethods()
                                                  .Single(m => m.ToString() == "System.Linq.IQueryable`1[TResult] SelectMany[TSource,TCollection,TResult](System.Linq.IQueryable`1[TSource], System.Linq.Expressions.Expression`1[System.Func`2[TSource,System.Collections.Generic.IEnumerable`1[TCollection]]], System.Linq.Expressions.Expression`1[System.Func`3[TSource,TCollection,TResult]])")
                                                  .MakeGenericMethod(typeof (LeftJoinIntermediate<TOuter, TInner>), typeof (TInner), typeof (TResult));

        var groupJoinResultSelector = (Expression<Func<TOuter, IEnumerable<TInner>, LeftJoinIntermediate<TOuter, TInner>>>)
                                      ((oneOuter, manyInners) => new LeftJoinIntermediate<TOuter, TInner> {OneOuter = oneOuter, ManyInners = manyInners});

        MethodCallExpression exprGroupJoin = Expression.Call(groupJoin, outer.Expression, inner.Expression, outerKeySelector, innerKeySelector, groupJoinResultSelector);

        var selectManyCollectionSelector = (Expression<Func<LeftJoinIntermediate<TOuter, TInner>, IEnumerable<TInner>>>)
                                           (t => t.ManyInners.DefaultIfEmpty());

        ParameterExpression paramUser = resultSelector.Parameters.First();

        ParameterExpression paramNew = Expression.Parameter(typeof (LeftJoinIntermediate<TOuter, TInner>), "t");
        MemberExpression propExpr = Expression.Property(paramNew, "OneOuter");

        LambdaExpression selectManyResultSelector = Expression.Lambda(new Replacer(paramUser, propExpr).Visit(resultSelector.Body), paramNew, resultSelector.Parameters.Skip(1).First());

        MethodCallExpression exprSelectMany = Expression.Call(selectMany, exprGroupJoin, selectManyCollectionSelector, selectManyResultSelector);

        return outer.Provider.CreateQuery<TResult>(exprSelectMany);
    }

    private class LeftJoinIntermediate<TOuter, TInner>
    {
        public TOuter OneOuter { get; set; }
        public IEnumerable<TInner> ManyInners { get; set; }
    }

    private class Replacer : ExpressionVisitor
    {
        private readonly ParameterExpression _oldParam;
        private readonly Expression _replacement;

        public Replacer(ParameterExpression oldParam, Expression replacement)
        {
            _oldParam = oldParam;
            _replacement = replacement;
        }

        public override Expression Visit(Expression exp)
        {
            if (exp == _oldParam)
            {
                return _replacement;
            }

            return base.Visit(exp);
        }
    }
}

Please make your life easier (don't use join into group):

var query = from ug in UserGroups
            from ugp in UserGroupPrices.Where(x => x.UserGroupId == ug.Id).DefaultIfEmpty()
            select new 
            { 
                UserGroupID = ug.UserGroupID,
                UserGroupName = ug.UserGroupName,
                Price = ugp != null ? ugp.Price : 0 //this is to handle nulls as even when Price is non-nullable prop it may come as null from SQL (result of Left Outer Join)
            };

If you prefer method call notation, you can force a left join using SelectMany combined with DefaultIfEmpty. At least on Entity Framework 6 hitting SQL Server. For example:

using(var ctx = new MyDatabaseContext())
{
    var data = ctx
    .MyTable1
    .SelectMany(a => ctx.MyTable2
      .Where(b => b.Id2 == a.Id1)
      .DefaultIfEmpty()
      .Select(b => new
      {
        a.Id1,
        a.Col1,
        Col2 = b == null ? (int?) null : b.Col2,
      }));
}

(Note that MyTable2.Col2 is a column of type int). The generated SQL will look like this:

SELECT 
    [Extent1].[Id1] AS [Id1], 
    [Extent1].[Col1] AS [Col1], 
    CASE WHEN ([Extent2].[Col2] IS NULL) THEN CAST(NULL AS int) ELSE  CAST( [Extent2].[Col2] AS int) END AS [Col2]
    FROM  [dbo].[MyTable1] AS [Extent1]
    LEFT OUTER JOIN [dbo].[MyTable2] AS [Extent2] ON [Extent2].[Id2] = [Extent1].[Id1]

For 2 and more left joins (left joining creatorUser and initiatorUser )

IQueryable<CreateRequestModel> queryResult = from r in authContext.Requests
                                             join candidateUser in authContext.AuthUsers
                                             on r.CandidateId equals candidateUser.Id
                                             join creatorUser in authContext.AuthUsers
                                             on r.CreatorId equals creatorUser.Id into gj
                                             from x in gj.DefaultIfEmpty()
                                             join initiatorUser in authContext.AuthUsers
                                             on r.InitiatorId equals initiatorUser.Id into init
                                             from x1 in init.DefaultIfEmpty()

                                             where candidateUser.UserName.Equals(candidateUsername)
                                             select new CreateRequestModel
                                             {
                                                 UserName = candidateUser.UserName,
                                                 CreatorId = (x == null ? String.Empty : x.UserName),
                                                 InitiatorId = (x1 == null ? String.Empty : x1.UserName),
                                                 CandidateId = candidateUser.UserName
                                             };