Hmm, the most meaningful games, a.k.a. Games Which Made Us Cry... here are my top three:
"Max Payne" (2001). Great storyline, great cut-scenes, great voice-acting and characters, tremendous sound-track, dynamite game-play.
"Metal Gear Solid 3" (2004). [Subsistence version of game] This needs no explanation. Kojima is simply a genius.
"Final Fantasy 12" (2006). Blows the roof off the RPG genre. Light-years beyond any of the other FF games, due to the subtlety and complexity of the characters, voice-acting, dialogue, scripting, and the geopolitical savvy of the storyline.