Getting to that last boss in Fire Emblem and keeping every single one of my characters alive as I pummle them into submission with my overpowered casters leading the charge for my super-fast, insanely-high crit swordmasters and main characters... is really satisfying. I play games like Fire Emblem because I want to need to finish the storyline and get to that happy ending.
Ghosting around and searching for enemies and encountering an enemy that sees me, so I quickly drop to prone as I go to my sights and blow his head off with my FAMAS, or if he doesn't see me, I switch to my USP and silently pick him off without his allies knowing. Or I'll be running around with reckless abandon with my UMP and dual 1887s, picking off any enemy unfortunate enough to encounter me. Or I'll be especially malicious and play my class labeled "TROLOLOL" which is infinite sprint/move faster/silent foot steps/riot shield/Magnum with tactical knife/throwing knife. I get SO MUCH RAGE MAIL when I use that class, its so satisfying ^_^
Getting every power-up, getting every piece of lore, and getting to the final fight with Dark Samus in the heart of Phaaze; something that has taken three games to do, and blasting the shit out of it 3 fucking times, so I can watch the cut-scene where Samus narrowly avoids being annihilated by the exploding phazon planet, and watch her take off her helmet and watch the sunset on the steampunk planet made of awesome... I can breathe a sigh of contentment and just enjoy the sunset with Samus.
For story driven games, its getting to the end of the story, solving all the problems, or getting the character's life back on track.
In multiplayer games, its being the better player, pissing off people who play unfairly, and making everyone around me go "woah... that guy is good ._."