The client runs on any Windows, Linux or Mac OS X machine. You also need a microphone. The server is mostly bandwidth bound, so as long as your network hardware is sufficient it should run on pretty much anything.
Please note that the Windows binaries distributed from SourceForge are compiled for SSE (Pentium 3 or Athlon-XP). Mumble is a VoIP solution for gaming, and as most modern games require at least that good a CPU it makes little sense for us not to optimize for it.