Final Fantasy I, IV, X, Tactics. FFI is just so basic and fun. FFIV was enjoyable, cause everyone died and came back to life for some reason. FFX is one of my favorite PS2 games. Tactics was different, and yet incredibly fun.
Kingdom Hearts II. Something about Black and White Disney mixed with Square Enix just rocks. Sephiroth battle was fun too.
Halo series. Incredibly fun, especially in a group. Kill Captain Keyes in Halo1 was incredibly amusing.
Elder Scrolls IV Oblivion is fun. It is so incredibly exploitable. I made 700 gold just by lying to a guy 3 times, and then turning him in once he told me to kill someone. I then grabbed all of his stuff, and sold it.
Super Mario I, III, and World were all incredibly fun. World was my favorite. Got it when I was 5. New Super Mario Bros. on the DS was also fun.
Sonic the Hedgehog 1, 2, and 3 were all classics. I also enjoyed Sonic and Knuckles. Sonic Rush 1 was fun on the DS.
Starfox and Starfox 64 were both incredibly enjoyable on Story Mode.
The original X-Men and The Simpsons arcade games are just great to play through with a bunch of friends on Senior Skip Day.
I often like to sit down and just play through an NCAA Football or Madden game. Franchise mode for hours upon hours is fun once every 3 years.
Star Trek: Armada, Star Trek: Elite Force, and Star Trek: Borg were all fun to play. I still install and play mods of Armada every once in a while. Still angry my dad beat all of these before I did.
Star Wars Jedi Knight Jedi Academy and Star Wars Jedi Knight Jedi Outcast were each fun. Exploding incredibly tiny aliens, so that their remains shoot up and you hear screaming is epic.
I have also played through a number of rhythm games. I played through every song on DDR Extreme on Heavy/Challenge, except for The Legend of MAX. Played through Guitar Hero, Guitar Hero 2, Guitar Hero 3, and a bunch of Guitar Hero custom games on Expert (Still have yet to beat Jordan, Through the Fire and Flames, and that one song on GH3 by Slayer on that list). I really <3 rhythm games.
I have enjoyed two online first person shooters. Unreal Tournament 2004 and Counter-Strike Source are each great to play. CSS makes me angry a lot, though.
My favorite genre is fighting games. I've won over $500 in cash, gift certificates, drinks, and t-shirts off of the Naruto: Gekitou Ninja Taisen (Naruto: Clash of Ninja in America) series. Guilty Gear is fun, but way too hard. Just reading 2H 6K 4P 3S 214P 6KK 4HH 3S 4K 236P is hard enough. Smash is enjoyable. Soul Calibur is fun, to an extent. Tekken gets boring after a while. Virtua Fighter is way too slow. Marvel vs. Capcom 1 is pretty fun, but 2 is no where near as fun.
And that is my assessment of what I have played over 19 years.