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I would like to learn a functional programming language to see a different programming paradigm.
My background in programming: Java (I have just passed the SCJP exam), some ruby and very limited Rails. I use bash for basic sysadmin tasks. I use Ubuntu 9.04.
As a second goal I would like to use fp to show kids (14-18 years olds) how math and cs interrelated. The guys are very good at programing (they are learning Python and Java at politechnical high school from the first year). However as tests show, they have difficulties with math esp. basic concepts of discrete math. I think we can develop their math skills by using programming (and I possibly that can be the topic of my teacher training thesis). I think a language with very basic vocabulary would serve this project best.
My vote goes to Scala or F#, which are both freely downloadable at the moment.
The advantage here is that they are mixed paradigm languages -- Natively they are functional languages, but you can also use imperative and Object Oriented programming. They also have large standard libraries -- Scala rides on the back of Java and F# has all of .NET, so you can program something interesting fairly quickly.
Scheme and Haskell are both pure functional languages, but unfortunately their standard libraries are relatively small, so it's hard-ish to do relatively common things, like parsing XML or scanning web pages.
I'd try Scala. It's not purely functional, it allows you to use a variety of approaches--but much of your java knowledge should port (It's JVM based) including the JDK libraries, and it's one of the most advanced languages I've ever seen.
If you're interested in learning language features and expanding your knowledge of how languages work, I couldn't imagine a better alternative.
I'm a big fan of Scheme, not least because the best book on it is freely available.