The melee attacks. Or, how-to-break-someone's-spine-with-a-single-kick.
Proximity mines. Instant-squad-kill plus the forshadowing beep of doom, just can't get enough of it.
The fight with Col. Vanek in Project Origin. Watch his expression turning from angst to utter horror, while throwing out Cluster F-Bomb, then subsequently get his head blown off is quite satisfying, given how much of a nuisance he and his ATC death squad has been to you up till this point.
Hearing Replicas, who are supposed to be ruthless supersoldiers, yelling out in fear at the sight of you.
A little more understated, but the moment you figure out in the first game that you can do jumping and sliding kicks that are instant kills against normal soldiers, not to mention the effect of knocking them across the room. Doing it in Slow-Mo on the last enemy in a squad is extremely satisfying.
There's a bit of delay allowed for jumping kicks, so you can hit first with the normal melee attack from your gun, then press the jump button and finish with a jumping spin kick.
The last hallucination in the first game. Seeing Alma screaming for her child, Harlan Wade's callous disregard for his own daughter, and the camera panning down to show her last name on the file, followed by reappearing in the darkness, and hearing Alma whisper in your ear, "I know who you are." That scene, and the terribly haunting, sympathetic music playing at the same time, is just chilling.
During the final APC sequence at Still Island, where Becket is holding off the Replica forces, this music plays. It's a perfect counterpoint, and it's awesome.