>Is it possible to do this for a Web application,

Sure.

>and if so, how?

Depends on what you want to achieve. Details, Rex! :-)

You can subclass Web Form controls (wait, can I say subclass in the .NET world or does it have to be derived?) and use those on your Web Forms, you can create whats called a User Control, or you can even create your own custom controls from scratch. Depending on what you want, you coudl use anyone of these three.