Anyways, YMMV. All I got to do once was set my Django application to run on Jython, and that was relatively painless.
Personally, I want to use a language implementation that will be around and (well!) supported for many years.
I guess all I'm saying is "convince me!" :) I'm all ears.
Why Functional Programming Matters: http://www.cs.utexas.edu/~shmat/courses/cs345/whyfp.pdf
Out of the Tar Pit: http://web.mac.com/ben_moseley/frp/paper-v1_01.pdf
Simple Made Easy: http://www.infoq.com/presentations/Simple-Made-Easy
Clojure's design goals combine some deep ideas about identity, state and time together and includes data structures and a concurrency API that supports these goals. It's going to be hard for anyone to just convince you in a comment like this, and even if they could, I'm not the one to do it as I'm a Clojure noob.
You should read this essay http://clojure.org/state and watch this talk http://www.infoq.com/presentations/Are-We-There-Yet-Rich-Hic....
I think you will find that Clojure is pretty interesting, even if you don't start using it right away. I apologize for just throwing you links, but I can't do it justice, and Rich Hickey is a great lecturer, so you'll get more from his stuff.
I think what Clojure can offer on top of that is macros, the advantages of which are really only evident on bigger or harder problems.
Its not so much about brevity or productivity as it is about correctness. Functional programming and immutable data makes it easier to reason about code and to prevent bugs/errors, especially in the context of concurrent/multicore code.