Well, depends on what you want and need. You are a .NET web developer and you are using C#. Though you may not use it I think knowing more than one language always gives you an edge, no matter what platform you are working on. I know VB and C# and though the two are very much alike I can sometimes use some C# for problems that are not as easy to solve in VB and vice versa. Learning a whole different non-.NET language might be even better. But sticking to .NET I'd say F# is a very good candidate. For web developers it is obviously a pro to know ASP.NET, HTML, perhaps Java, Javascript, PHP, CSS, XML (and all come with their own sub-techniques and languages)...
So let's say you do not wish to learn another language or you already know all languages you should know about. In .NET there are
LightSwitch[
^] and
Silverlight[
^] that can help you build powerful web applications. And while you're at it you might as well learn to work with the cloud using
Azure[
^]...
As if that is not yet enough there is
WCF[
^] for building (a.o. web) Services.
Other stuff ANY programmer should know are basic principles, such as Object Oriented Design (
SOLID[
^],
Design Patterns[
^]), basic knowledge of their framework (in your case the .NET Framework which is so immense that you will never be able to grasp it all) and perhaps other issues such as
parallel programming[
^].
In .NET knowing stuff like
LINQ[
^] can make you more valuable as you can get things done fast and in an elegant way.
And of course you will need to interact with a database. Knowing any sort of database (and I guess your best bet is a
Relational Database[
^]) is a must. SQL and Oracle are both good candidates. Of course you must also be able to communicate with these databases. Having a solid understanding of
ADO.NET[
^],
ORM[
^]'s and possible specific ORM's such as
Entity Framework[
^] certainly gives you an edge.
Being able to work with other frameworks, libraries and third party tools can also help. Just to name a few
MEF[
^],
Microsoft Enterprise Library[
^] and
DevExpress[
^].
Does all of that scare you? Don't worry! No one will expect you to know all of those languages and techniques (I certainly don't), but they all give you an edge. I say pick one that suits you, play around with it and move on when you think you know enough. In my opinion being an all-rounder is better than being a specialist. Know what is out there and try some of it.