1st Game Played (as far as I can remember): Super Mario Brothers w/ Duck Hunt + Gun (duh !) back in 1990 or so I believe, perhaps 1989, I'm not sure about that, but I got my SNES only the year that followed if I remember correctly. I might have played a video-game before that but if so I can't recall ... s'been too long ago.
2nd, Best: Such a difficult question. I cannot answer with just one title or one series, but I will answer by a simple logic, which means giving the series' name that certainly sucked more time in my life than anything before except a real job, which would be Diablo II: Lord of Destruction. I played that game from day one (in fact D2 Classic before the expansion) up to when I completely stopped only two months ago (and by completely stop I mean literally throwing the CD's in the waste basket along with the manuals and everything). That game was more like a drug than anything lately, but when I first played it I really had the feeling that I was playing the single absolute best game in my entire video-gaming life.
If I had to give honorable mentions there'd be plenty, as other "best" games I played, but I must at least name one, which has to be the Warhammer 40,000: Dawn of War games, especially with Dark Crusade, which in my humble opinion results in the very best RTS game available to date on any platforms, closely followed by the Command & Conquer series.
3rd, future: I am awaiting Crysis and Bioshock at the moment, with the latest being released this month.