As a web programmer do I need to learn any more languages to enhance my career? I work in a .NET environment and am good at C#, but have zero skill in VB. For client side scripting I use javascript, jQuery and PrototypeJS.
Should I learn any more languages or do you think that what I know is enough for web programming?
Yes.
It's always a good thing to learn new language, new paradigms, new philosophies, new whatever knowledge or way of mind you can find. It will always be useful in a way or another later.
Other languages are always helpful to broaden your mind as you expand your influence in your career. Knowing how other languages accomplish things gives you useful options in your "home" environment.
Dive into some PHP, or C/C++, or go deep and learn LISP for fun. But don't bother with VB. :)
I wouldn't necessarily worry about learning new languages for the sake of learning new languages. You should be aware that other technologies exist and when and where they are used. What's more important is your ability to solve problems and deliver solutions.
Having said that, if you can show you have a basic understanding of other languages it will stand you in good stead, as you won't be starting from zero.
Yes. Just generally. If you need to ask this question, then the question should be which one, not whether there should be one.
F# is within your stable, but sufficiently (i.e. completely) different. Given that you can create assemblies that your web application can dynamically load, I would suggest that you not feel constrained by "web languages".