Try Clojure Online (in a web browser)
A Server-side Implementation
Raynes (Anthony Grimes), a surprisingly young and prolific Clojure hacker, put together Try Clojure.
It looks like so:
and executes a reasonably wide variety of Clojure code. As I understand, it operates using a well-sandboxes Clojure instance running on a server somewhere.
A JavaScript Implementation
Another approach to this idea is to implement a good-enough subset of Clojure in JavaScript, and run that entirely in a web browser. The only example of this I know of is here but I don’t know how complete it is.
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.