Without reading anyone else's posts and thereby tainting the jury, here are my favorites:
Sonic The Hedgehog 1 and 2 - Sonic was the first game I had because it was the pack-in when I got my system. I used to hate Sonic 2 until I realized that you can disable Tails in the options menu.
Streets of Rage II - Might be my all-time favorite video game.
Bare Knuckle III Fan-Translation - Sooo much better than Streets of Rage 3.
Golden Axe - Also one of the first Genesis games I ever played. I also remember playing the arcade cab at a Round Table Pizza BitD.
Ghouls N' Ghosts - Needs no explanation.
Kid Chameleon - Neat platform game, but is LOOOONG as f*ck and has no save option.
Ayrton Senna's Super Monaco GP II - Because Ayrton Senna.
Columns - I used to just look down on it as a Tetris rip-off but it's actually a cool game. Neat atmosphere, too.
Joe Montana Football - Arcade-style play. Really easy (like Tecmo Bowl) so you can run the score up like a mofo.
Comix Zone - Beat-em-up with an interesting premise and cool graphics.
Buck Rogers: Countdown to Doomsday - Really cool (and fairly short) American-style RPG (mostly conforms to D&D rules.)
Starflight - Hard to explain, except to say that it's awesome.
Batman - Side-scrolling action game.
Madden 93 & 94 - The two best Madden games. "John Madden Football" is also cool to check out because it was the first Madden game made for a home console.
Street Fighter II Championship Edition - Needs no introduction.
Fire Shark - Vertically-scrolling shooter.
Phelios - Vertically-scrolling shooter with an ancient Greek theme.
NBA Live 95 - My all-time favorite basketball game (though I prefer to play it on SNES).
NHL Hockey (All of them) - I like the first 4 for different reasons, but they are all fun. After that, they were all the same game with roster updates, but still fun.
PGA Tour Golf I, II, III, and European Tour - Some of the best golf sims ever made. NHL 96 is the only shitty one on the Genesis.
Insector X - Insect-based shooter.
Virtua Racing - Choppy and dated, but impressive technologically for it's time.
Turrican - I f*cking love this game. Unfortunately it is impossibly hard and is more fun to play with cheat codes. But the levels are so fun to explore that it's still worth it.
Truxton - Classic vertically-scrolling shooter.
Altered Beast - The first pack-in game. Aged very poorly, but if you can put yourself into the mindset of someone who has been playing nothing but 8-bit games and just bought a Genesis at launch, you can appreciate the huge step forward, technologically.
Thunder Force II - Another launch game. Levels switch between horizontal scrolling and 360 degree scrolling. Best Genesis game available on launch day, by far.
Saturday Night Slam Masters - Cartoony arcade-style wrestling at its best.
Crue Ball - Pinball with digitized Motley Crue music. f*cking awesome.
Championship Pro-Am - Sequel to R.C. Pro-Am series on the NES. Same gameplay with better graphics and sound.
Virtual Pinball - Make your own pinball tables, much like Pinball Construction Set. Was developed by the same guy (Bill Budge.)
Sunset Riders - Port of a classic Konami arcade beat-em-up.
