Using only closures you can build an OO system, with what looks like an OO syntax. I believe that Smalltalk's OO system works like this. Definitely Lisp's CLOS does.

I'm not so sure that I'd say that CLOS needs to use closures to quite the extent you imply. Take a look for example at the Closette implementation found in The Art of the Metaobject Protocol. I think it's an exaggeration to say that this uses only (or even primarily) closures to do its work.

Update

In reply to tilly's update :-) (Let me first qualify that IANALI - I am not a Lisp implementor - take me with the appropriate grain of salt.) Certainly it's possible to do the same thing with closures. And I cheated a little bit - the Closette implementation is a simple one that has a few problems which AMOP suggests are probably overcome using closures. But I'd be surprised if any widely used CLOS implementation is largely in terms of closures - I'd expect it to be more the melange of imperative, OO, and functional programming that is Common Lisp (and that is evidenced in Closette). It wouldn't surprise me, though, if some of the Scheme object systems out there were a little more functional, and if anyone around here knows, it'd be interesting to know how its done in OCaml, which is a much more functional language than CL.