AWT is the OS-specific part of UI rendering on desktop, not on the Web side of things in which JSP, Servlets etc. live. A bit more specifically, things like Swing (which has those JPanels, JButtons and so on you mentioned as UI components) and SWT are currently based on AWT and work on top of it to render the UI and allow it to work as expected.
Unfortunately all this means you can't use AWT based components on Web pages since, well, Web pages are (usually) platform agnostic in the sense that they don't get to decide exactly how parts of the UI are rendered, there's just a pile of markup which is treated as a sort of plea to the Web browser to do things the Web designer hopes for without 100% quarantee that the end result will be what the designer wanted.
There's been a lot of reinventing the wheel to achieve Swing/AWT kind of UI creation on the Java's Web side since it's a clever model, like you seem to already know Google Web Toolkit tries to do its part to make Web seem more like a desktop application while in reality it merely automates the needed JavaScript Ajax underneath to make the web page behave as if it was a desktop application. One another framework for this is Tapestry which I haven't personally used but some think it's a decent choice too.
And then there's of course my personal favorite Apache Wicket which allows you to have a true separation between Java code and markup and it behaves quite similarly to Swing UI code too! In fact there's a whole bunch of name collisions with Swing's UI component classes for the most simple things. Assuming you're any familiar with coding a desktop application UI I strongly recommend Wicket, it abstract away the boring and tedious parts (Servlets, URL resolving, page bookmarkability, security...) and replaces them with an event-driven model similar (but not equal) to Swing's EDT which is where the desktop UI magic would normally happen.
While this is going completely away from what you're looking for, with Wicket you can create such a set of POJO Web components that you can reuse them just about anywhere and thus get what you asked for. A word of warning though, Wicket assumes you really know how to code with Java and some laughably easy things may be tedious at first but in the end you should be quite happy with what you got.