Hitting the charge blade finisher combo in Monster Hunter 4 always felt satisfying for me (once I figured out how it worked )  Something a bit more recent, I love hitting Cloud's finishing touch in Smash 4.  It just feels like it has so much impact and it can kill at relatively low percents

Still to this day it has to be Kingdoms of Amalur: Reckoning simply because the combat finishers felt so satisfying, despite them being button mashing finishing moves they still rewarded you with XP but also a graphic final move. The other nice aspect of the game is that each class with their different weapons all have their own unique finishing moves, most of them (like the one in the gif) remind of of Mortal Kombat.

Off the top of my head, I can safely say this is one

https://youtu.be/COsdpIwVd9g?t=25s

Only those who've played it can understand why this was so satisfying. Might come up with something else later.

I always considered Anima's Overdrive "Oblivion" in FFX to be my favourite attack. First of all the character design is badass, and secondly the attack destroys entire parties with ease. What a shitty way to go though - getting punched repeatedly by some angry hairball that is fused to the bottom of a very angry fish-mummy-wrap-chained thingy.
Couldn't find a gif for it so here is a picture of Anima; I'll try to find a gif later

*edit* Here are all of the aeon overdirves in ffx; all very badass, but Anima [2:14] is the best 

https://www.youtube.com/watch?v=o-TAnVgsWnY

Any coordinated teamfight in Dota2 with perfectly timed spells between your team is the most satisfying thing in gaming.

Landing a fire blast on a Pokémon with a x4 weakness to Fire, it just feels SOOOOOOOO GOOD

also this 

https://www.youtube.com/watch?v=1xyHZLmyQ2c

Shooting for the first time with a Dreadnought in EVE online.
Now that was unlimited power !