An addictive game for me would be something I would continue to come back and play excessively, even as it became older over time. For that, it would have to be either The Elder Scrolls: Morrowind or Chrono Trigger.
Asheron's Call, because even for it's old outdated graphics, thru thick and thin, MMORPG after MMORPG, I keep going back to it. I have played DDO, Lord of the Rings Online, Star Wars Galaxies, Lineage 2, World of Warcraft, and countless others, but Asheron's Call just has such a much more advanced loot system, and second to none freedom of movement (both in PvM and PvP), that I can't escape the clutches of the game.