Resident Evil/Resident Evil Director's Cut, Resident Evil 2/Resident Evil 2 Dual Shock, Resident Evil 3: Nemesis -- these three are the main three. They are for originally PS1, GameCube, and some are on PC. Then you have GameCube Resident Evil 4, despite this being a great game, sadly it paved the way to the bastardization called Resident Evil 5. Resident Evil 4 is always for PS2 and Wii.
Those are the main games. Then you have Resident Evil for the GameCube (a REmake) Resident Evil 0, Resident Evil Survivor, Resident Evil Code Veronica, Resident Evil Code Veronica X, Resident Evil Files I and II, Resident Evil Dead Aim, and Resident Evil Umbrella Chronicles and Resident Evil Darkside Chronicles. Which these titles range from PS2, GameCube, PC, and Wii. Also you have Resident Evil Archive Files on the Wii.
L3ggy will fill in any I happened to miss.