Jake,
It sounds like you have some web development experience. As you might have some time between jobs to learn new things, now might be a good time to focus on a particular technology.
The current trend in Web applications seems to be the notion of Web 2.0 or even 3.0 technologies. It would benefit you to learn more about Rich Internet Application development. To start off, you could learn how to use Flex and Actionscript. The Flex SDK is free and both Eclipse and Netbeans have plugins for Flex. The Glassfish server is also an easy to install JEE application server that can be used for your application's server related needs. Note: It's always easier to find UI developer positions rather than server side developer positions. Flex and Actionscript make it really easy to learn Web UI (no more messy Javascript or Ajax). Your knowledge of Java and OO skills will help you in the new environment.
Once you have the presentation layer all squared away, you can focus on the server side technologies. As mentioned previously, Spring is an excellent framework to get to know. It will provide you with opportunities to learn more about dependency injection, aspect oriented programming, and another MVC framework. Besides you also have experience in JEE environments that can be enhanced with the use of Spring.
The other technology that is very good to know would be XML and all related technologies such as XSLT and XSD. This in turn will make it easier for you to understand how to write configurations for Spring, Hibernate, Ant, Maven, etc. XML is also used in Web Services to define services for Applications that are involved in service oriented architectures. You could also learn to use JAXB (Java to XML Binding) which will come in handy when you need to send XML from the server to your presentation layer as in AJAX or even in Flex.
Best of luck,
-Sharon Miller