This is just off the top of my head, so I'm sure I'm forgetting some of my favorites. There are just so many must play Sega games.
Master System
-RPG:
Phantasy Star
-Adventure/Platforming
Sonic 1,2&Chaos, Wonder Boy in Monster Land, Wonder Boy III, Alex Kid in Miracle World, Alix Kid in Shinobi World
-Action
Fantasy Zone
Genesis
-RPG
Phantasy Star II,III,IV, Beyond Oasis, Crusader of Centy
-Adventure/Platforming,
Sonic 1,2,3,Knuckles, Ristar, Dynamite Heady, Contra Hard Corps., Castlevania Bloodlines, Wonder Boy in Monster World, Shadow Dancer, Shinobi 3, Revenge of Shinobi
-Fighting
Street Fighter 2 Turbo, Eternal Champions, TMNT Hyperstone Hiest
-Action
Gunstar Heroes, Jurassic Park Rampage Edition, Subterranea, Red Zone, Zero Tolerance,
-Horror
Splatterhouse 2,3,
-Strategy Shinning Force 1,2, Herzog Zwei
-Racing
Virtual Racing
Sega CD
-RPG
Lunar, Lunar 2 Eternal Blue
-Adventure/Platforming
Snatcher, Knuckles Chaotics, Sonic CD, Monkey Island
-Fighting
Eternal Champions
-Action
Rebal Assault
-Strategy
Shinning Force CD
Saturn
-RPG
Panzer Dragoon Saga, Albert Odyssey
-Adventure/Platforming
Astral, Pandemonium, Croc, Tomb Raider, Nights Into Dreams
-Fighting
Virtua Fighter 2, Virtua Fighter MegaMix, Last Bronx, Dead or Alive, Fighting Vipers
-Action
Burning Ranger, Panzer Dragoon, Panzer Dragoon 2 Zwie, Virtua Cop 1&2, House of the Dead
-Horror
Resident Evil, Enemy Zero, Deep Fear
-Strategy
Shinning Force 3
-Racing
Daytona USA CCE, Sega Rally CE, Wipeout 1&XL
Dreamcast
-RPG
Grandia 2, Skies of Arcadia, Phantasy Star Online, Silver, Omikron The Nomad Soul, Record of Lodoss War
-Adventure/Platforming
Stupid Invaders, Elemental Gimmick Gear, Shenmue 1&2, Sonic Adventure 1&2, Shadow Man, Soul Reaver, Eccor the Dolphin
-Fighting
Virtua Fighter 3TB, DOA 2, Project Justice, Marvel Vs Capcom 2, PowerStone 1&2, Bleem: Tekken 3
-Action
Rez, Mobil Suit Gundam: Rise from the Ashes, Headhunter, House of the Dead 2, Bleem: MGS, Jet Grind Radio Sword of the Berzerk: Guts Rage, Alien Front Online
-Horror
Resident Evil Code: Veronica, RE2&3, Carrier, IllBleed, Dino Crisis, D, Alone in the Dark
-Racing/Driving
Crazy Taxi 1&2, Sega Rally 2, Daytona USA, Looney Toons Space Race, Tokyo Extreme Racer 1&2, Metropolis Street Racer, Sega GT
