Choosing which language to use when developing ASP.NET applications is both easier and harder than choosing a language for classic ASP development. It is harder because it may be intimidating for some to choose between a substantially revised Visual Basic and a completely new language, C#. It is easier because the choice of language no longer requires giving up substantial amounts of functionality for your preferred language.
As in many other cases, including language choice in classic ASP, a lot of the decision is determined by where you're coming from. If you're:
You'll probably prefer Visual Basic.NET.
You'll want to look at C# or JScript.NET (keeping in mind that finding code examples in C# is easier, since the novelty of the language makes it more interesting for many).
Visual Basic.NET is the obvious choice, but you may also find it worthwhile to check out C#, which offers a lot of the power of C++ without such a steep learning curve.
You'll probably feel right at home with C#, which, as a C-derived language, shares a lot of syntax with these languages.
Visual Basic.NET will probably be easiest to learn, although C# runs a close second.
Because of the level of cross-language interoperability in .NET, your choice needn't be an either/or. You can feel free to create applications and classes in Visual Basic.NET, C#, JScript.NET, or any .NET-enabled language, knowing that they will be able to work together smoothly and easily, thanks to the CLR.