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Just curious.
For me:

Genesis (Known as Mega Drive, here in Brazil) :
Sonic the Hedgehog 1-2-3, obviously.
Golden Axe (I loved to play this with my friends).
Ecco - The Tides of Time (Even if it was scary for me at the time, it was a fun game).
Captain America and the Avengers (Another good game to play with friends).
Rambo III (I was a fan of rambo at the time. Exploding choppers with a bow was fun).
World of Illusion Starring Mickey Mouse and Donald Duck.
Toejam & Earl (Crazy game! A pity they don't make games like this anymore).

Super Nintendo (Or Snes) :
Super Mario World (Like Sonic, it's a game you MUST play if you have the console).
Contra 3: The Alien Wars (Incredible hard, but a awesome game nonetheless).
Super Mario Kart (Fun race game. Even for me that I'm not a big fan of race games).
Super Bomberman 4 (Another game that I loved playing with friends).
International Superstar Soccer (I generally don't like soccer games very much. Not my cup of tea, I guess. But this one is very good!)
Metroid 3 (Samus FTW! Only bad part in the game that I remember, was having to learn how to make the Jackie Chan's jump in the walls. Arrrgh! The frustation!!!)
Sixteen bit games, huh? Alright.

Genesis:
--Streets Of Rage
--Sonic The Hedgehog 2

Super NES:
--Donkey Kong Country
--Super Mario World
--The Legend Of Zelda: A Link To The Past

Technically-16 bit games on PS1:
--Final Fantasy Chronicles/Anthology/Origins
I only ever had an 8-bit console, then jumped to PS2.
However on a mate's Mega-Drive and SNES I loved Golden Axe, Sonic (only played 1) and on his SNES (and arcade) I loved Mortal Kombat 2 and Killer Instinct.
Well, my Atari St was a 16 bit computer so... Castle Master, Ikari Warriors, Populous (&the promised lands), Dragon Spirit, Indiana Jones % temple of Doom, Sidewinder...
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Drelmanes: Just curious.
For me:

Genesis (Known as Mega Drive, here in Brazil) :
Sonic the Hedgehog 1-2-3, obviously.
Golden Axe (I loved to play this with my friends).
Ecco - The Tides of Time (Even if it was scary for me at the time, it was a fun game).
Captain America and the Avengers (Another good game to play with friends).
Rambo III (I was a fan of rambo at the time. Exploding choppers with a bow was fun).
World of Illusion Starring Mickey Mouse and Donald Duck.
Toejam & Earl (Crazy game! A pity they don't make games like this anymore).

Super Nintendo (Or Snes) :
Super Mario World (Like Sonic, it's a game you MUST play if you have the console).
Contra 3: The Alien Wars (Incredible hard, but a awesome game nonetheless).
Super Mario Kart (Fun race game. Even for me that I'm not a big fan of race games).
Super Bomberman 4 (Another game that I loved playing with friends).
International Superstar Soccer (I generally don't like soccer games very much. Not my cup of tea, I guess. But this one is very good!)
Metroid 3 (Samus FTW! Only bad part in the game that I remember, was having to learn how to make the Jackie Chan's jump in the walls. Arrrgh! The frustation!!!)
You mention the Genesis without saying Phantasy Star II-IV, for shame!
Shadowrun (SNES)
Warriors of the Eternal Sun (GEN)
Zool 2. And anything Psygnosis.
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tejozaszaszas: Well, my Atari St was a 16 bit computer so... Castle Master, Ikari Warriors, Populous (&the promised lands), Dragon Spirit, Indiana Jones % temple of Doom, Sidewinder...
I'll add Dungeon Master and Carrier Command to those. Man, I loved that old ST.
Bah, the ST was a ripoff of the Amiga 1000. Speaking of both, there were a ton of great PD and indie shareware games back then. Like Scorched Tanks and Wibble World Giddy and Galaga Deluxe.
As a kid I owned a SNES; never played the Sega Genesis. I enjoyed many of the same games common to everyone who played it (Super Mario World, Zelda, Street Fighter 2), but these were my favorites:

Super Castlevania. Still the best of that series and one of the best side-scrollers of all time. It was my favorite SNES game just for the sheer enjoyment of gameplay, ambiance, and music.

Super Punch-Out, which I actually enjoyed more than the classic NES version. I felt it was a little more fair in the twitch department. I liked the circuits better, and not needing to play repeat turbo-charged versions of past opponents, which I always thought was lazy. If they were this good all along why were they mugs in the Bush-league circuit?

Knights of the Round Table, which I thought was pretty entertaining for a side-scrolling beat 'em up. The medieval motif went a long way.

Super Ghosts and Goblins, much like Super Punch Out, I enjoyed this sequel better than the NES classic, as I thought it was pretty much an improvement in every meaningful way, and challenging without being sadistic about it, which I hated about the original.

F-Zero. An old friend and schoolmate of mine were obsessed with that game for months, in a tightly contested battle of breaking each other's records, sometimes by hundredths of seconds. By far the most I ever got into a video racing game, console, computer, or otherwise.

Rampart. My favorite strategy game released on that console. Most SNES ports of arcade games were piss-poor watered down ersatz versions, but the port of Rampart was pretty well done. Graphically not quite as good as the cabinet-box original, but solid nonetheless.

Good times. I also owned a Playstation 1 in high school (the last time I bothered with consoles), but I have fonder memories of the SNES.
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rasufelle: Streets Of Rage
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saramakos: Killer Instinct.
Ahhh... I forgot about those. Great games, indeed!
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Drelmanes: ...
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orcishgamer: You mention the Genesis without saying Phantasy Star II-IV, for shame!
Never played these games through the end, so I can't comment on them. If that makes you feel better, I have a Sega games collection PS2 disc (This one), in wich the Phantasy Star games are included, so I can try beat them, if you recommend it so much.
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saramakos: Killer Instinct.
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Drelmanes: Ahhh... I forgot about those. Great games, indeed!
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orcishgamer: You mention the Genesis without saying Phantasy Star II-IV, for shame!
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Drelmanes: Never played these games through the end, so I can't comment on them. If that makes you feel better, I have a Sega games collection PS2 disc (This one), in wich the Phantasy Star games are included, so I can try beat them, if you recommend it so much.
If you somehow "missed" playing III you might not be missing much, II and IV are outstanding, though.
SNES:
- The Legend of Zelda: A Link to the Past.
- Secret of Evermore
- Chrono Trigger
- Final Fantasy IV & VI
- Illusion of Time

Genesis:
- Sonic the Hedgehog I, II & III
- Sword of Vermilion
- Story of Thor
- Jurassik Park: The Lost World
ah 16-bit games, a era i am actually fairly familiar with :P

SNES
Super Mario World
The Legend of Zelda: A Link to The Past
Donkey Kong Country 1-3(if you like 2d platformers you must play all of these and if you can only play one of them play the second one)
Chrono Trigger
Secret of Mana
Axelay

Genesis
Phantasy Star 2-4
Shining Force 1-2 (just finished a session of the first one less than 20 minutes ago)
Sonic The Hedgehog 1-3 & Knuckles
M.U.S.H.A (excellent shooter)
Gunstar Heroes
Super Mario World - The Best Platformer Ever (tm)
Final Fantasy IV
The Lost Vikings
Super Castlevania
Ogre Battle: March of the Black Queen
The Legend of Zelda: A Link to the Past

Honorable mentions to:
Street Fighter II
Rock N' Roll Racing
TMNT IV: Turtles in Time