NetHack.
While each particular game of NetHack is finite (still VERY hard to complete though), the levels and item identifications are randomly generated for each game. It also feature permadeath, so every time you die, you have to start over at level 1 with a new game.
In two decades of playing computer games, no game has ever come close to NetHack in terms of sheer addictiveness (even WoW, and that game is like crack).