How do I check if a type provides a parameterless constructor?

The Type class is reflection. You can do:

Type theType = myobject.GetType(); // if you have an instance
// or
Type theType = typeof(MyObject); // if you know the type

var constructor = theType.GetConstructor(Type.EmptyTypes);

It will return null if a parameterless constructor does not exist.

If you also want to find private constructors, use the slightly longer:

var constructor = theType.GetConstructor(
  BindingFlags.Instance | BindingFlags.Public | BindingFlags.NonPublic, 
  null, Type.EmptyTypes, null);

There's a caveat for value types, which aren't allowed to have a default constructor. You can check if you have a value type using the Type.IsValueType property, and create instances using Activator.CreateInstance(Type);

type.GetConstructor(Type.EmptyTypes) != null

would fail for structs. Better to extend it:

public static bool HasDefaultConstructor(this Type t)
{
    return t.IsValueType || t.GetConstructor(Type.EmptyTypes) != null;
}

Succeeds since even enums have default parameterless constructor. Also slightly speeds up for value types since the reflection call is not made.

Yes, you have to use Reflection. But you already do that when you use GetType()

Something like:

var t = x.GetType();
var c = t.GetConstructor(new Type[0]);
if (c != null) ...