Is there an "Empty List" singleton in C#?

Enumerable.Empty<T>() is exactly that.

You are looking for Enumerable.Empty<T>().

In other news the Java empty list sucks because the List interface exposes methods for adding elements to the list which throw exceptions.

I think you're looking for Enumerable.Empty<T>().

Empty list singleton doesn't make that much sense, because lists are often mutable.