Probably not as much as you’d think! We use a cluster for offline indirect light probe baking on Watch_Dogs – as far as I know it’s just a cluster of regular machines though, no special hardware. At my last studio we used a cluster of blade servers for doing content builds on every checkin, as well as assisting developers’ builds (we had an awesome distributed content build pipeline). We also had a lightmap baking cluster that was just a bunch of unused machines that we hijacked and installed Linux on, but that was all very jury rigged.
As for the "sexy" stuff, game physics & rendering is realtime by nature so using clusters doesn’t really make much sense for that. However some places do use the commodity GPUs in their clusters to accelerate processes with CUDA or OpenCL as well as using the CPUs. And it’s commonplace to do distributed code builds using unused dev machine cycles (see Incredibuild or SN-DBS).
But in general I don’t think there’s a lot of call for dedicated HPC hardware in the development process. Studios are a lot more likely to have extra old/unused development PCs (usually pretty high spec), so it makes sense to put them to good use instead.
Of course it’s probably a different story for cloud gaming like OnLive or Gaikai, as well as the servers needed for MMOs & multiplayer games, but hopefully someone else can fill you in about those.