I think we should just keep series together to make it simpler. Even though we all have personal favorites amongst the series, they're all the same concepts.
I'm probably forgetting a lot, but here's mine. I'm not going to list the platforms, because most have a lot, or they're obvious which ones I'm talking about. No order.
Super Mario Bros.-An absolutely classic series. No explanation needed.
Grand Theft Auto-An extremely controversial series that changed gaming. The cheats added a ton of replayability as well.
Halo-Didn't have an Xbox, and wasn't a big fan of Halo 3, but there's no question this deserves to be in this list.
Starfox-Never owned the game, but always played it at friends and cousins' houses. Great replay value.
Pacman-I was never good at this game really, but it's still played a ton to this day.
NBA Jam-Like Justice said, it inspired a bunch of later games to be made with the same concept. Traded
Crystal Pony for this game.
MVP Baseball-Spent a full summer just playing MVP 2005. One of the best sports games of all time. The prospects and farm system depth was amazing, and it's a shame it's not made anymore.
Goldeneye 007-Great campaign, and possibly the best multiplayer game of all time. I loved the codes as well. Probably my favorite game of all time.
Mortal Kombat-Another controversial game which was my personal favorite of all the fighting series at the time. Nothing trumps fatalities.
Tekken-Never really liked the console games myself, but loved the arcade one. My second favorite of the fighting series.
Mario Kart-The best N64 game IMO, and probably my second favorite game of all time.
Pokemon-EVERYONE played this game, no matter how old you were. Too bad it expanded to 23423424 Pokemon, or however many they have these days.
Sonic-Can't decide which I like best, I even loved Sonic Spinball. Up there in my favorites.
Doom-Controversial, revolutionary, amazing multiplayer. Everything you can ask for in a video game.
Call of Duty-Great campaigns, incredible multiplayer. I've put over 15 days into COD4 online, so there's no way this doesn't make my list.
Tetris-Simple, but addicting. Played by everyone, and on basically anything with capable technology. Nothing beats seeing those giant rockets after completing an amazing game.
Honorable Mention:
X-Men-A personal favorite. These Genesis games were incredible to me, since I was a big X-Men fan. I forget which one was good and which sucked, but I had the one that sucked, so I was forced to play the good one everywhere but my house.
Altered Beast-Another personal favorite. Played it so much, it broke. Bought it again a few years back on Amazon, and still had fun playing it.