When I read the thread title, my first thought went to Borderlands. I see it's not quite in the spirit of what this thread is actually about, but I'm going to explain my answer.
Borderlands vanilla has a level cap of 50. When you beat the game (which takes you to about level 35,) you get "playthrough 2" where everything is souped up in level, much the same as playing Nightmare on Diablo. When you win on Playthrough 2, it further ups the enemies so that almost all of them are at or around the level 50 cap. Some call this Playthrough 2.5.
Because Borderlands is a Diablo clone with an FPS skin, even after the game is over, it's still fun to run around the world, killing stuff and maybe getting better equipment randomly. I would enjoy playing the game with my max level character just 'cause.
Then the third expansion, General Knoxx came out. It raised the level cap. However, the only areas in the game that were above level 50 were the expansion zones. There was no additional reraising of the enemies once you left, so your ability to continue to enjoy your character was confined literally to the last zone or two of the expansion because everything pre-xpac was trivial, and really so was everything leading up to those last two zones WITHIN the expansion. I played the game incessantly before the expansion, and then when I got it, downloaded it and beat it, I basically stopped playing the game because there was no longer anything to do. Besides Arena.