Only 3 huh...
1) Gran Turismo 2 (PS1) - despite its bugs the game took everything that was great from original and turned it up a notch with more cars, more tracks and rally events. I played this game for hours and even built two fan websites dedicated to it. In fact I organized one of more comprehensive FAQs for the game.
2) Demon Stalkers
(C64) - a Gauntlet clone but with more puzzle and maze solving. 99 level of inspired design, like a room full of locked one-way doors were you could see the exit but had to plan every move with chess like thinking since keys were limited. Some levels required you to back-track up two levels before continuing down. Others were fight to death, button mashing blood baths, contrasted with level that required you to never fire a shot in order to get out as quickly as possible. I'd love a remake of this on the iPad.
3) Tomb Raider II (PS1) - the graphics were amazing (at the time) and it was first game I played were you really felt like you were INSIDE an interactive 3D world. Also the game went on forever and I almost cried when it was over because of the time invested in beating it.
Honorable mention (sorry I had to do it)
Sonic the Hedgehog (Genesis) - with no saves beating the game start to finish was HOURS of platforming madness. For a 16-bit game the speed, color and music was light years ahead of 8-bit Mario.
Daytona USA (Saturn) - once you got the feel for each car you could pull amazing drifts at insane speeds. Plus who can forget that sound track?
Gran Theft Auto: Vice City (PS2) - While GTA III was a mind blowing sandbox experience GTA:VC had everything I loved as high schooler in the 80s: the music, the cars, even the landscape was spot on... and I should know I've lived in South FL my whole life. Plus this game actually had a story line were as the first game seemed like a random collection of to-do-tasks.
If any of these games got stuck in their respective systems I could careless... I could play them over and over again.
BTW the PSN version of Daytona USA sucks because the other cars (Black, Yellow, Orange, Pink, Green) seem to be missing and the sound track has been changed