Well I don't do this anymore, so limiting to a game or two is kind of impossible for me... I've just got too many games and not enough time (or justification for the time) to spend on them. But I'll run the gauntlet for your viewing and nostalgia pleasure.
Compelling Games that I Used to Play Habitually
The numeric Sonic's (mostly the first... only completed it recently -- ty PS2 save-state)
Sonic Spinball
Tiny Toon Adventures (another Genesis title)
Star Wars: Galactic Battlegrounds
Heroes of Might and Magic 3 Demo (my brother and I were obsessed with it like you wouldn't believe... finally ponied up the money for it on GOG, beat the very first campaign level and really haven't touched it too much since -- it's not really any wonder though, we pour massive amounts of time into grinding peaks out of our characters, so it's a bit of a frightening investment of time)
Crash Team Racing
Crash Bash
Gran Turismo 3
NHL titles (played 2002 the most, but used to play any version given the chance)
Ratchet and Clank (mostly Up Your Arsenal)
Double Dragon (Master System)
Pokemon (Blue and Ruby are pretty much the extent)
DDR Max 2
Tony Hawk (and Disney Extreme Skate Adventure -- Hey the mechanics were solid!)
Driver
Tale Spin (Genesis again)
Super Smash Brothers (all of 'em -- only own Brawl though)
If I still played games in this manner, I would probably mostly play MW2, StarCraft and DDR (choice, I know). Of the games that I would put up a fight against replaying anymore they would be: Pokemon, which I find to be way too much of a chore; and Battlegrounds, because I played the utter crap out of it and playing it online or through LAN is pretty much impossible.