There are "silicon oscillators" that claim to be MEMS, though it's unclear what structures they use (and how they're temperature compensated). They are usually programmable, which seems to suggest there's a PLL and P/Q divider or DDS to generate the output.
Certainly, this approach gives better universality to an otherwise fairly fixed and narrow design (i.e., you can only make the MEMS elements so large before they're impractical, or so small before they're unusable). They get better ROI, if not necessarily better performance as a result (if the PLL suffers from phase noise outside of the loop bandwidth, or if the DDS suffers from excess jitter). That said, they're usually comparable to, or better than, cheap crystal oscillators.
I don't see MEMS filters offhand, though SAW could arguably be called a similar technology. Mechanical filters (made from, I think, nickel or terfenol as transducer, and various mechanical resonator bits) had been common back in the day.
Tim