One alternative to leveling that has proven to be very viable in an MMO setting is collecting. Gods and Heroes has the a game mechanic that lets you collect "minions" to engage in squad based combat. The Agency has what Smedley called a "living loot" system where you collect operatives to work with you. Guild Wars makes collecting skills a part of the game.
I'm hoping this becomes more commonplace and that more MMOs use collecting as a means of 'advancing' your character, instead of levels.
One of the great things about Guild Wars was that veteran players were often not that more "powerful" than new players; because collection was one of the principle means of "advancing" your character, but the items you collected weren't necessarily "better" than another, how you strategically used the skills/heroes/etc. was more important than your level.
I found Metal Gear Portable Ops to be a highly addictive game because of this mechanic. As well, in Guild Wars, many players often went after quests to obtain skills that they had no real interest in using, simply to be completists.
Magic the Gathering had it right: collection can a powerful enough motivator to keep a user subscribing that can help level the playing field between new and old players, helping avoid the issue of mudflation, and it also can add more strategic elements to the game play (assuming you are restricted in the number of items from your collection that you can use at any one time.)