IIRC, Sandia Lab's SUMMiT V process (the source of videos like [1]) was funded in part to make mechanical latches and fail-safes for nuclear weapons, but I'm not sure what's currently in use for obvious reasons. I don't think they found many other practical applications, though experimentation led to TI's DMD chips, among other things.
Occasionally, MEMS techniques are used to make (relatively large) gears for watches.
I've also seen people try to use gears for microfluidic pumps, but I don't think any are much better than current simpler solid-state approaches.