I have hundreds (though I won't bore you with them all!)
Ghosts n Goblins being my favorite arcade game. On holidays I'd always be looking out for it and begging the parents for the money to play it.
Dungeon Master - the amount of time I spent with half my party dead to realise what the altar of rebirth actually meant!
Turrican 2 - pretty much everything about that game was amazing!
Treasure Island Dizzy - first Dizzy game I played and I've played pretty much all of them since!
Kick Off 2 - whilst Microprose soccer on the C64 was my favorite footy game at the time - KO2 on the Amiga was just amazing
Bubble Bobble - the amount of time, on the C64, I've spent with my brother trying to beat this game is untrue!
SWoS - can't have KO2 without SWoS being mentioned - to have all the teams and all the players amazed me - the manager option was just amazing
Elite 2: Frontier - I was addicted to this game for a good while - nearly getting Elite status. Most of my time was spent trying to get all the passes to the planets, etc.
If we are talking specifically consoles then:
Resident Evil on the PS1 - this was one of the reasons I got the console, amazing game, hard as nails at times and the jump scares were epic
Metal Gear Solid - superb game where by you could hide in a box, so obvious but really well done, swopping the controller ports over for the psychic fight, so many good ideas
M.