The legacy of kain series showed to me the potential games had for portraying truly epic story lines, i was utterly distraught when i found out they wouldn't be making the finale. The voice acting is to this day the best i have ever heard in a game.
Final Fantasy X also had one of the best stories and characters i have ever experienced. It had its flaws but the storyline was just head and shoulders above the majority of games.
Silent Hill is another game that showed it was possible to do some things better in games than you ever could in other forms of media, it is to this day the scariest thing i have ever experienced.