Sadly, not many, which is a shame because there are a lot of good ideas out there. Unfortunately the MK team and quite a lot of fans don't think things like frame advantages and decent hit properties are worthwhile, because it would be ripping off other games or something equally ridiculous.
Counter hits seem to have been added though (somewhat), which you could argue came from any one of a number of games.
Aside from that and and the multi-tiered arenas, nothing springs to mind.

Hara Kiri--->Samurai Shodown
Multi Tier Environments--->DOA and so on
Puzzle Kombat--->Puzzle Fighter (not a fighting game, I know)
Counters--->Crap load of games, most notable Alpha counters from SF and Combos breakers from KI
Deathtraps (or in a non literal sense, ring outs)--->Virtua Fighter
That's it for now.

For some reason I think they got the death trap idea from Unreal Tournament; that game had alot of creative maps with traps in em. ya neva know!