The main consoles that marked the generation were: Sega Dreamcast, Sony PlayStation 2, Nintendo GameCube and Microsoft Xbox.
The games that marked the generation were: Shenmue(Dreamcast), Sonic Adventure(Dreamcast), GTA San Andreas(PlayStation 2),Shadow of the Colossus(PlayStation 2), Final Fantasy X(PlayStation 2), God of War(PlayStation 2), Max Payne(PlayStation 2), PES(PlayStation 2), Call of Duty(Xbox), Red Dead Redemption(Xbox), Halo(Xbox), Super Mario Sunshine(GameCube), Metal Gear Solid(GameCube), etc.
Sega Dreamcast(1998)
PlayStation 2(2000)
GameCube(2001)
Xbox(2001)
God of War(2005)
Halo: Combat Evolved(2001)
Metal Gear Solid 3: Snake Eater(2004)
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