As some others have mentioned, learning some frameworks and tool combinations are quite helpful. The Spring and Hibernate combo is probably the most prevalent that you'll see out there.

Swing is a pretty rare skill these days, as it's not used by that many. I saw a mention of JSF in the comments, and that hasn't caught on much either. If you are looking for the best way to get employed in Java, Spring and Hibernate and the overall CS background is helpful (the books mentioned in this thread are all recommended to most Java pros). JavaScript should be helpful.

As others here recommended, learning another language is also recommended. I wrote this article recommending to Java pros that they learn a new lang (http://jobtipsforgeeks.com/2012/07/11/advice-from-a-jug-lead...), and I'd still recommend it. Fewer young engineers seem to be gravitating to Java.

Checking out Python, Scala, Ruby and Clojure would always be helpful, and in many environments these days you will be exposed to more than one language anyway.

You've got lots of choices at this point. Keep control of your career prospects by not limiting your technical diet to what your fed at work.