Genesis

(Part 1)
Alien Soldier
Alisia Dragoon
(Disney's) Aladdin    
Arcus Odyssey
Art of Fighting
Battle Mania 2- TS vintage (two different translations exist, both at the same site)
Battletoads, Battletoads & Double Dragon
Beyond Oasis
Captain America & The Avengers
Castle of Illusion starring Mickey Mouse
Castlevania: Bloodlines
Chakan: The Forever Man
Chiki Chiki Boys
Columns, Columns III: Revenge of Columns
Comix Zone
Contra: Hard Corps
Crusader of Centy (AKA Soleil)
Cyborg Justice
Darius II (AKA Sagaia)
Dashin' Desperadoes (only really recommend if you do 2-player)
Decap Attack
Devil's Crush MD/Dragon's Fury
Donald in Maui Mallard (aka Maui Mallard in Cold Shadow)
Double Dragon
Dr. Robotnik's Mean Bean Machine (Puyo Puyo 2 for cutesy japanese version)
Dynamite Headdy (translation exists for unaltered japanese version, which is a bit easier)
Earthworm Jim, Earthworm Jim 2
Ecco the Dolphin
El Viento
Elemental Master
Empire of Steel (aka Steel Empire)
Fatal Fury, Fatal Fury 2
Fire Shark
Flashback: The Quest for Identity
Forgotten Worlds

(Part 2)
Gaiares
Gain Ground
Gargoyles
General Chaos
Ghouls'N Ghosts
Gley Lancer (Translation available)
Golden Axe, Golden Axe II
(The) Great Circus Mystery: starring Mickey and Minnie
Gunstar Heroes
Gynoug (AKA Wings of Wor)
Herzog Zwei
High School Soccer Kunio Kun
Jewel Master
Joe & Mac
Kid Chameleon
King of the Monsters, King of the Monsters 2
King Colossus (Translation exists)
Landstalker
Light Crusader
Lightening Force: Quest for the Darkstar (Thunder Force IV non-US title)
The Lost Vikings
M.U.S.H.A.
Madou Monogatari
Mega Bomberman
Mega Man: The Wily Wars (Rockman Mega World for 60 FPS, otherwise change country settings)
Mega Turrican
Mercs
Michael Jackson's Moonwalker
Mickey Mania: The Timeless Adventures of Mickey Mouse
Mutant League Football, Mutant League Hockey
NBA Jam Tournament Edition
(The) Ooze
Out of this World
Panorama Cotton
Phantasy Star II, Phantasy Star III: Generations of Doom, Phantasy Star IV: The End of the Millennium
Phantasy Star II: Shilka's Adventure,  Anne's Adventure, Huey's Adventure, Kinds's Adventure (translation exists)
Pirates! Gold
Pulseman (Translation available)
(The) Punisher

Quackshot starring Donald Duck
Raiden Trad
Rainbow Islands
Ranger X
Rent A Hero (if you know japanese)
Ristar
Rock N' Roll Racing
Rocket Knight Adventures
Samurai Shodown
Saturday Night Slam Masters
Shadow Dancer: The Secret of Shinobi, Revenge of Shinobi, Shinobi III: Return of the Ninja Master
Shadowrun
Shining Force, Shining Force II
Shining in the Darkness
Soldiers of Fortune
Sonic 3D Blast
Sonic Spinball
Sonic the Hedgehog, Sonic the Hedgehog 2, Sonic the Hedgehog 3 & Knuckles
Spider-Man & Venom: Separation Anxiety (only really recommend if you do 2-player)
Splatterhouse 2, Splatterhouse 3
Streets of Rage, Streets of Rage 2, Streets of Rage 3
Strider
Sunset Riders (only really recommend if you do 2-player)
Super Fantasy Zone
Super Street Fighter II
Surging Aura (don't need to know japanese, but it might help)
Teenage Mutant Ninja Turtles: The Hyperstone Heist
Thunder Force III
ToeJam & Earl, ToeJam & Earl: Panic on Funkotron
Traysia
Twinkle Tale (translation exists)
Undead Line
Warsong (graphics patch exists), Langrisser II (Translation exists)
Wonder Boy III: Monster Lair, Wonder Boy in Monster World, Monster World IV (translation exists for IV)
World of Illusion starring Mickey Mouse and Donald Duck
Yu Yu Hakusho: Makyo Toitsusen (AKA Sunset Fighters) (Translation exists)
Ys III: Wanderers from Ys
Zombies Ate My Neighbors    

Nearly all patches found here- http://mijet.eludevisibility.org/