I'm still behind, but gaining fast!
Open-ended campaigns are my preferred approach to RPGs. I would rather run a game this way then any other.
Games that are not designed for long term, open-ended campaign play absolutely serve a purpose, and have a definite place in ones gaming collection. There are a number of them on my own shelves.
While it is possible to run my own game, The Googly Eyed Primetime Puppet Show, as a long term game with no definitive end, I fully don't expect that's what people are going to do with it. It, like Toon, Teenagers from Outer Space, Hunter Planet, Fiasco, and many other fantastic RPGs, serves best as a break from the usual, and familiar.
However, any game which focuses on exploration of the setting(s), and the characters, where power creep is relatively slow, or at least manageable, and you can change things up from time, to time without throwing the whole thing out of whack works for me for open-ended play.
I especially like games where the PCs are people living in the universe of the game. These are some of the best games for open-ended play because the players are following the lives of character who are native to the setting, and as such they may live, work, have adventures, get married, have kids, grow old, and die like real people. You are then able to play their kids, or grand kids. Life goes on, as they say, and a virtual life does the same except with space travel, magic, and more explosions.
My favorites for this type of game include:
Star Trek, using Last Unicorn's ICON System, RPG.
Traveller, using my Classic/MegaTraveller hybrid rules.
Champions, 4th edition of course, for Supers that keep on trucking.
and while D&D isn't my favorite game by any stretch, I do concede that it is well built for open-ended, long term play.
Others I've had success with include Star Wars (WEG D6), Villains & Vigilantes, Mutants & Masterminds, Mekton, and Teenagers from Outer Space (yeah, I know what I said, but it's possible to use the game for longer term play if you really want to).
OK, that's it for that. What's next?