Personally, I've always been a fan of games that never really end.
- The Civilisation series.
- numerous Microprose simulations.
- The Football Manager series.
- MMOs (WoW & Eve in particular).
None of these ever finish and as such have more replayablility (if that is an actual word).
Of the games that I own that do 'end', very few have made me want to. Notable exceptions being Half Life 1, 2 & the episodes so far, Deus Ex, the first KOTOR game.
I think, what I'm trying to say in a very round about way, is that a lot of games are failing to create any kind of narrative that are making players *want* to finish them and the games that succeed despite this lack of narrative are ones in which the player creates it him/herself.