void in C# generics?

You cannot use void, but you can use object: it is a little inconvenience because your would-be-void functions need to return null, but if it unifies your code, it should be a small price to pay.

This inability to use void as a return type is at least partially responsible for a split between the Func<...> and Action<...> families of generic delegates: had it been possible to return void, all Action<X,Y,Z> would become simply Func<X,Y,Z,void>. Unfortunately, this is not possible.

No, unfortunately not. If void were a "real" type (like unit in F#, for example) life would be a lot simpler in many ways. In particular, we wouldn't need both the Func<T> and Action<T> families - there'd just be Func<void> instead of Action, Func<T, void> instead of Action<T> etc.

It would also make async simpler - there'd be no need for the non-generic Task type at all - we'd just have Task<void>.

Unfortunately, that's not the way the C# or .NET type systems work...

Here is what you can do. As @JohnSkeet said there is no unit type in C#, so make it yourself!

public sealed class ThankYou {
   private ThankYou() { }
   private readonly static ThankYou bye = new ThankYou();
   public static ThankYou Bye { get { return bye; } }
}

Now you can always use Func<..., ThankYou> instead of Action<...>

public ThankYou MethodWithNoResult() {
   /* do things */
   return ThankYou.Bye;
}

Or use something already made by the Rx team: http://msdn.microsoft.com/en-us/library/system.reactive.unit%28v=VS.103%29.aspx