A positive sign: there is an article on InfoQ about "one of the first published reports of Clojure being used in a large-scale production deployment." It doesn't appear to be open, but at least it is a sign of Clojure being used in a mission critical application in the real production world. A big step for the Clojure community.
Take a look at Compojure. It's a web framework written in Clojure, so it allows you to write and run (on an embedded Jetty) useful web apps in Clojure, and also serves as a good example of a sizable chunk of real-world Clojure code.
It's under active development and has a helpful Google Group.
I think that Compojure is probably the best way to go for an example. I doubt it's a "medium sized" example, but there's probably subsections of it that are small that would work. At least, that's going to be my approach. smiles
which is a small m.u.d. client prototype built in clojure, the advantage being that it's totally self-contained, and probably pretty simple, including the concepts involved. Documentation, eh, it's jus' alright, but the concepts in the code tie very closely to the action elements of the M.U.D. that runs easily.
We're two years on from this question and, whilst that's still early in the cycle for a language, Clojure is definitely being used for serious production work. At World Singles, we have several thousand lines of Clojure in production that handle all sorts of general purpose tasks in our web platform - I blogged about this in my Real World Clojure series.
For some reasonably large open source projects - not exactly applications, but high-profile infrastructure - you could look at Storm from Twitter and Cascalog from BackType (now part of Twitter). 4clojure.com has been mentioned as an open source web application, that's worth a look too, but note the new github repo for 4clojure.
I can only recommend you to check out Pedestal, a very promising web framework, both server-side and client-side (where it facilitates ClojureScript). The gui stuff is a bit hard to grasp, but quite much the way it should be done to stay sane in a large app.