1. The Ultimate Stuntman (NES) Not a great winner for story here with mega slugs, evil androids, bomb disposal and such, but this is to games what 80's action movies are to cinema: Entertaining (often ridiculously so) breezy and full of well...action.
2. Super Mario Bros. (NES) The hero's journey. Mario pursues a goal in the face of opposition. Forget the lack of mentor characters (does the little mushroom guy count?). I enjoy this game for its purity of storytelling, and increasing odds as you advance to your ultimate goal: Rescuing the princess! Simple, but timeless.
3. Half-Life (PC) because of the sense of isolation the game creates and moments of discovery that are player made for the most part (unlike the sequel where other - invincible - characters not so subtly nudge you in the right direction). It really takes advantage of the first person format and feels cinematic in all the right ways without becoming bogged down in "creating moments". They just happen.