I like the epiphanies I experience in games. Those "aha!" moments when all the puzzle pieces fit together and you realize you've cracked the code. Sometimes this happens in a boos fight, and sometimes it happens in every boss fight; Shadow of the Colossus. I refused to use a walkthrough in that game, and I spent over an hour and a half on one boss before I figured out how to climb onto him. But once I did, man, awesome feeling.
The treasure hunter sidequest in Red Dead is the most recent game I can think of that does that. Just riding along my horse when all of a sudden something looks familiar; a tree, a road crossing, a ridge. Yanking back on the reigns, pulling out the map, and thinking this could indeed be it. Hopping off the horse, looking around to match the angles, and finally searching around for the x that marks the spot. Genius.
I also like "oh snap!" moments in games, where I'm legitimately blown away by something, ala The Battle of Endor mission in Rogue Leader. Akbar comes over the intercom, informs me it's a trap, pull a 180 to confront the oncoming fleet. Targeting computer on, wing formed, looking for available targets. One pops up, then another, then a squad, then another squad, and in a matter of a few seconds the targeting computer completely lights up the screen. Oh snap. There's... too many of them!
Yeah, those are probably the best moments.