Try Clojure Online (in a web browser)
A Server-side Implementation
It looks like so:
and executes a reasonably wide variety of Clojure code. It operates using a well-sandboxed Clojure instance running on a server.
Another site, 4clojure, has a set of online micro-problems (“koans”) helpful in learning Clojure.
How about an Applet?
It should be reasonably straightforward (though perhaps involving a tedious download delay) to run a Clojure REPL in a Java Applet, thus making it possible to start working with Clojure right away using only (well, mostly) your web browser. But I haven’t see such a thing yet.