1) Gran Turismo 2, on the PSX (remember when everyone called it that, instead of PS1?) I loved the cars and racing, and then found out about creating hybrids (using a cheat device like a gameshark to put parts from one car into another). Hybrids really opened the game up for me. I played that game constantly for half a decade, exploring all the possibilities of hybriding. Tons of fun. Everything from little boxy subcompact cars with 64000 hp to realistic alternate trim levels of classic muscle cars...tons of fun.

2) Uncharted Waters, on the SNES. Age of sail/exploration/trading game, with a little piracy if you want to go that route. The first game, not the second one where you choose from multiple characters. I played that game through so many times and learned how to handle the mechanics so well that I could reliably get the most difficult to recruit characters extremely early in the game, and worked out all sorts of trade routes to get money quickly. Sugar from Lisbon to Bordeaux, where you get porcelain, which sells for a good price everywhere else. Run that little trade route a few times until the value of the items start going down, and go from there. I would always circumnavigate the world several times not because it was required (it wasn't, ever), but because I was such a little nerd that I found it fun to map the entire world. Also utterly destroying both Spain and Turkey's merchant fleets and then the battleships they would send to hunt me down...so fun.

3) World of Warcraft. More addictive than fun, really, especially with the way the game has turned more and more toward a daily grind of the same bunch of quests, repeated for every. single. character. you want to keep active. I do find creating new characters and running through different starting areas fun, though.

Honorable mentions go toward Skyrim (PC), Minecraft (PC), Left 4 Dead (PC), Final Fantasy 7 (PS1), Grand Theft Auto 3 (PS2), and Legend Of Zelda: A Link To The Past (SNES), but most especially to The Elder Scrolls 3: Morrowind (Xbox, then PC). Before Skyrim, before Oblivion, there was Morrowind...the first time I played it was mind blowing. The fact that you were essentially thrown out into this enormous, open world and could do pretty much anything you wanted was shocking at the time. It was the first real sandbox game I played, unless you count Uncharted Waters. Spent hours and hours messing around in that game.