The first real game I played was Command&Conquer: Tiberium Sun in 2000. What a fantastic first game to play it was, I was hooked from there and have not looked back since. Continued to explore driving simulation(Need for Speed), RPG(Dungeon Seige, Titan Quest, Morrowind), RTS(Warcraft series, not WoW rubbish, Command&Conquer series, Supreme Commander) and FPS games(CS, TF2, Battlefield, Call of Duty, Half-Life).
For consoles I really can't remember which one I had but I enjoyed Mario Brothers, Battle Tanks and Adventure Island the most. After that on to some Sega console to play Mortal Combat and Sonic. Besides those games I never really got into console gaming, didn't care much for the restrictive game pads and the lack of diversity(lacking RPG, RTS and FPS games at the time) so I became a PC only gamer.