River City Ransom - Fun in single player and awesome in co op. Has aged pretty well (graphics/music) and still plays great.
Super Mario Brothers 3 - Laid the groundwork for future iterations of the series with its overworld map. Clean, attractive graphical style, solid play control, great level designs, etc etc. As much fun today as it was when it first came out.
Mario 64 - Showed how 3d platforming should be done. Still one of the top 10 (possibly even top 5) examples of the genre.
Fallout - Highly replayable, nonlinear, and somewhat open 2d RPG with attractive sprite-based graphics, a well written story (accompanied by solid voice acting), and an intuitive combat system. Somehow it manages to maintain a solid pace and sense of cohesion no matter what path you choose to complete the game in (unlike its sequel, which was also loaded down with too many in-jokes).
Half Life - Integrated storytelling and level design in ways that hadn't been done before. Unreal did the level connected to level idea before and Sin did the story-intensive gameplay before, but neither interwove both together with such success. Unreal still had Bluff Eversmoking, which was a great level with a nice mystery regarding the location of the escaped prisoner, but that doesn't compare to the whole experience that Half Life offered (also expanded upon in the various expansions and sequels).
Crazy Taxi - Ultimate risk/reward, pickup and play game. Easy to learn/ difficult to master, and it doesn't matter who you are, you'll have fun playing it. Even the lackluster PS2 port is fun as hell to just kick back and play for a while. WHY IS THERE NOT A VERSION FOR PSP? Oh well, at least the PSP has Outrun 2006 Coast 2 Coast (which is the only other driving game I'd nominate).
I'm not much of a fan of Final Fantasy 7 for a variety of reasons. Inconsistent art direction, bad localization, overemphasis of graphical effects instead of playability (hi, unskippable summons), trite character design, etc. It was very much a typical jrpg that was simply at the right place and right time with just the right marketing push.