Alright...brace yourself:
[Game Boy/Game Boy Color:]
The Legend of Zelda: Link's Awakening - adventure (not sure if you should go for the normal or "DX version", don't know what the differences are..)
The Legend of Zelda: Oracle of Ages - adventure
The Legend of Zelda: Oracle of Seasons - adventure
Metroid II: Return of Samus
Super Mario Land - platformer
Super Mario Land 2: 6 Golden Coins - platformer
Wario Land: Super Mario Land 3 - adventure/platformer
Wario Land II - adventure/platformer
Wario Land 3 - adventure/platformer
[Game Boy Advance:]
Castlevania: Aria of Sorrow - adventure/plaformer/RPG
Castlevania: Circle of the Moon - adventure/platformer/RPG
Castlevania: Harmony of Dissonance - adventure/platformer/RPG
Final Fantasy I & II: Dawn of Souls (graphical updated ports of the original 2 for the NES) - JRPG
Final Fantasy IV Advance - JRPG (obviously all of these are graphical updates of the originals..)
Final Fantasy V Advance - JRPG
Final Fantasy VI Advance - JRPG
The Legend of Zelda: The Minish Cap - adventure
Metroid Fusion - adventure/platformer
Metroid: Zero Mission - adventure/platformer (major, major update of the original from the NES...also includes the original as an unclockable[I think])
Sonic Advance - platformer
Sonic Advance 2 - platformer
Sonic Advance 3 - platformer
Super Ghouls N' Ghosts - adventure/platformer (ported from SNES version w/ an a additional/optional level path consisting of levels from the Genesis version[which is basically the 2nd one in the series]...so, I guess it's "sort" of a combination of the 2nd and 3rd ones, but more towards the 3rd than anything[so 2nd is still worth playing!])
Super Mario Advance (basically graphical update of original for NES, the rest are graphical updates of their originals as well)
Super Mario Advance 2: Super Mario World
Super Mario Advance 3: Yoshi's Island
Super Mario Advance 4: Super Mario Bros. 3
Wario Land 4 - adventure/platformer
[N64:]
007: Goldeneye - FPS
Perfect Dark - FPS
Super Smash Bros. - fighter
[NES:]
Castlevania 3 - adventure/platformer
Contra - action/platformer
Ghosts N' Goblins - adventure/platformer
The Legend of Zelda - adventure
Mega Man - action/platformer
Mega Man 2 - action/platformer
Mega Man 3 - action/platformer
Mega Man 4 - action/platformer
Mega Man 5 - action/platformer
Mega Man 6 - action/platformer (all the original Mega Man games are bloody sadistic, so may or may not be your cup of tea...also, I think there are graphical updates of some of these games[at least the first 3 under the guise of Mega Man: The Wily Wars for the Genesis, so may wanna check that one out if you go for these..])
Ninja Gaiden (another sadistic series lol!)
Ninja Gaiden 2: The Dark Sword of Chaos - action/platformer
Ninja Gaiden 3: The Ancient Ship of Doom - action/platformer
[Sega CD:]
Sonic CD - platformer (one of the greatest Sonic games ever, imo)
[Sega Game Gear:]
Sonic Chaos - platformer
Sonic Triple Trouble - platformer
Tails' Adventures - adventure
[Sega Genesis:]
Contra: Hard Corps - action (funny, the one in the series released on a Sega platform[unless there are others on other Sega platforms] I consider to be the most superior in the series!!....TRY TO GET ALL ENDINGS[4 + 1 secret ending!])
Earthwrom Jim - action/platformer
Earthworm Jim 2 - action/platformer
Ghouls N' Ghosts - adventure/platformer
Gunstar Heroes - action (somewhat similar to Contra imo, more quirkier though and less gritty)
Mickey Mouse: World of Illusion - adventure/platformer
Rocket Knight Adventures - platformer
Shining Force - strategy RPG
Shining Force II - Strategy RPG
Sonic 3D Blast - platformer (not everyone's a fan of this one[probably due to the isometric view] but I personally enjoy it a good bit)
Sonic the Hedgehog - platformer
Sonic the Hedgehog 2 - platformer
Sonic the Hedgehog 3 & Knuckles - platformer (technically you can play Sonic the Hedgehog 3 and Sonic & Knuckles individually, but trust me, the combined experience of both games is superior![HYPER SONIC FTW! XD])
Sparkster(a.k.a. Rocket Knight Adventures 2) - adventure/platformer
Streets of Rage - beat' em up
Streets of Rage 2 - beat' em up
Streets of Rage 3 - beat' em up
Teenage Mutant Ninja Turtles: The Hyperstone Heist - beat' em up
Tinhead - platformer
Thunderforce III - shoot' em up
Thunderforce IV - shoot' em up
Toejam & Earl in Panic on Funkotron - adventure/platforming? lol
Wonder Boy in Monster World - adventure/platformer/RPG (pretty fun imo, even though I never beat it XD)
Zool: Ninja of the Nth Dimension - platformer (released on other platforms[originally for the Amiga] but this is the one I remember playing)
[Sega Master System:]
Alex Kidd: The Lost Stars - platformer
[SNES:]
Clock Tower - survival horror/point-and-click adventure (Japan only; was later ported to PC and Sony Playstation as 'Clock Tower: The First Fear')
Contra III: The Alien Wars - action/platformer
The Legend of Zelda: A Link to the Past - adventure
Mega Man X - action/platformer
Mega Man X 2 - action/platformer
Mega Man X 3 - action/platformer
Sparkster - adventure/platformer (yes, the versions for the Genesis and SNES are different enough to warrant a play of each if you're interested)
Super Metroid - adventure/platformer
Super Mario All-Stars - adventure/platformer/compilation (includes first 3 original Mario games for the NES w/ updated graphics and The Lost Levels(the "real" Super Mario Bros. 2, the one you see for the American one is actually a palette swap of a game called Doki-Doki Panic...er, something like that...I DON'T KNOW THE FULL STORY, LEAVE ME ALONE!! X3)
Super Mario Kart - racing (..obviously, lol)
Super Mario World - adventure/platformer
Super Mario World 2: Yoshi's Island - adventure/platformer
[Sony Playstation:]
Castlevania: Chronicles - adventure/platformer (major graphical update of the original NES one or Super Castlevania IV for the SNES[I think], not sure)
Castlevania: Symphony of the Night - adventure/platformer/RPG (the original "Metroid"-styled Castlevania...Though there's a port of it to the PSP w/ additional features, the convenience of emulation of an earlier console is nice, don't ya' think? *whistles*)
Clock Tower - survival horror/point-and-click adventure ('Clock Tower 2' in Japan)
Crash Bandicoot - adventure/platformer
Crash Bandicoot 2: Cortex Strikes Back - adventure/platformer
Crash Bandicoot: Warped - adventure/platformer
Final Fantasy VII - JRPG
Final Fantasy VIII - JRPG
Final Fantasy IX - JRPG
Silent Hill - survival horror
Tomba! - adventure/platformer/RPG
Twisted Metal 2 - action?
I'm not terribly good w/ attributing some genres to some games so you'll have to forgive me for that!! XD Also, sorry for pointing out blatantly obvious ones as well as some possible incoherent descriptions(I got flustered listing all the ones I could possibly remember growing up and look theming up[to be certain of certain versions and such]). Anyways, I'm sure there's a heck of a lot more I could list, but I think this is good enough for now!! XD
P.S: I also figured it'd be pointless to list the same games on multiple systems(unless they were different enough, such as in the case of 'Sparkster'), so you may find more than one version of some games in your ROM-hunting.