This is a very hard question, I guess Super Mario Bros. (and sequels up to Super Mario World, the DS game (NSMB) sucked ass compared to the rest) is one of the most significant games I've ever played but then there's also games like Warcraft or Diablo, the first The Sims, the Monkey Island series of games, Breath of Fire II, Civilization, Phoenix Wright and Castlevania (Metroidvania) are one of the few recent games, Ocarina of Time, Day of the Tentacle, Seiken Densetsu 3.
And there's probably a bunch I've forgotten but those are among the best games I've played ever, they are all from 2000 downwards except the recent (or future) sequels of Warcraft, Diablo, Civilization and the relatively recent Metroidvania and Ace Attorney games.
Oh crap I almost forgot a very important one, the Marathon Trilogy.
While I enjoyed a lot of the games in the PS2 era, I don't think any of them made an impact big enough as the games listed above.