At the moment I use SVN to manage java source code. Is there a solution out there whereby I can check in code and have the new code automatically compiled into a JAR file? Somehow the check in would need to trigger the compile process.
You need a continuous integration tool. Hudson would be a good choice (I've been using it the past year and it works really well)
You could do this with a CI server; the server can sit on another machine (the build server) and get the latest commit, build it, and compile it to a JAR. (Of course, this isn't really ideal, on large projects [due to lots of changes being submitted, and so on], but on personal things it should work to a reasonable degree).
There are a number of continuous integration programs which do this very thing. Two I've used are Bamboo (commercial) and CruiseControl (open source). Bamboo is about 1000x easier to setup then CruiseControl, and really pays for itself after you've created a hundred build plans or so. With CruiseControl you will have killed yourself long before you get to your hundred build plan.