Hardcore Casual asks how important are levels? Well, for most MMOs, its pretty much everything. The level IS the game. You have this exponential growth curve to the level cap and then levels are replaced by gear, which is pretty much the same thing, except prettier. The fact that they are just a substitute for levels is especially obvious when they do it with a blatant progression in mind.
Why do we have levels? Well, players need a goal. And making your numbers bigger becomes that goal.
But levels also come with disadvantages... one major disadvantage is that it creates a gulf between haves (people who have been playing a while) and have-nots (newbies) that tends to deter new players from joining the game. As a game ages, more and more people end up at the tail end of the level progression, and it slowly dies as people leave and no one new joins. It also means that no matter how populated your server is, you still have very few people you can group with at any one point in time, since everyone might be a different level. (Mentoring/sidekicking are nice little hacks that help avoid this issue to some degree.)
Another disadvantage is that it renders old content obsolete as people progress. Older zones become static, empty wastelands because everyone already beat the content.
What else can we do to provide players with a sense of progression besides "levels"? Well, not much, really. At least not for role playing games where the notion that you start off weak (the amnesiac adopted peasant boy) who grows up to be strong (along the way finding out you are the son of a god or the illegitimate son of the King and only heir to the throne, or both, who knew) is part and parcel to the genre, and so there has to be some arbitrary thing in game to measure your progression from subpar to super. Whatever you call it, that arbitrary measure is the "level."
But we can implement the leveling concept differently... the most significant flaw in most existing models is that it prevents a lot of the player base from playing together.
I was disappointed to see that Warhammer Online, with its PVP focus (which is a pretty powerful carrot on a stick right there) decided to create a lengthy level based grind. Couldn't PVP leaderboards be the incentive to play better and longer? Did we really need regular ranks (levels) AND Renown Ranks? If we just had Renown Ranks people would start off at mostly the same degree of power (Renown Ranks of course let you train and become more powerful, but not exponentially like the regular levels do), so they would still provide a powerful incentive to keep playing (making that Renown Rank numbers go up) while avoiding the principle drawbacks of leveling (players not being able to play together.) Imagine being able to log in from the very beginning and group with grizzled veterans on the battlefields! Keep imagining, because that's not what you're going to get if you actually log into WAR. Instead, you get empty chapters, empty PQs, and people spread thinly across each chapter and each tier, you'd never know there were thousands of players online with you, because you'll never see more than a handful at a time unless you jump into a Scenario. In Scenarios, you get to see BOTH handfuls, one handful playing Order and the other Destruction.
Another way to avoid the pitfalls of the leveling mechanic is to have a mechanism that makes people restart frequently; this could keep the game friendly to new players much longer. I can picture a game where your objective is to collect henchman/pets that you can level and gear up separate from your main character (the distinction being that the main character wouldn't need levels - and experienced players would have an incentive to play with inexperienced players when leveling up a new pet.) While leveling a pet would involve the on-rails movement through the world that we have today, if every player periodically has to start over from the beginning (with a new pet), that means the old world is constantly in use, and no part of the world turns into the complete wasteland that most MMO starter areas become shortly after launch.
Also, I think we'll see more collection mechanisms in the future, such as the collectable skills in Guild Wars. Even though each skill are relatively equal in power to another skill of the same type (Elite or normal), and grabbing more skills doesn't necessarily make a character more "powerful," it does make the player more flexible, so you still have a sense of progression. That same drive is what makes games like Magic: the Gathering work. You might not be more powerful than someone else because you buy the whole store display case, but it does give you a great deal more flexibility to create the kinds of decks you want (or "need.") Similarly, Guild Wars, even after hitting the level cap, still motivated people to keep playing to unlock skills to gain additional flexibility in the metagame: creating different builds.
But the ultimate, and least grindy, way to measure a character's progression is: story. Story is why most single player games don't feel like a grind, even if they involve the same kind of repetitive gameplay. Bioware is getting a lot of attention for promising to bring story into MMORPGs. Guild Wars did that too; the mission based progression was a powerful motivator to keep playing. For me, the missions were my "levels." It was only once I finished all of the missions for the Prophecies campaign that I began to lose interest in the game, and I moved on. And, I guess, that's why we get numbers instead of story. Bigger numbers are easier to implement. And if you decide you want your players to stick around longer, you just need to throw in bigger numbers, and most of them will.
Back in the MUD days, story based games were far more common. But it was a lot of easier back then when the only limit to what you could put in game was your English ability. I guess we won't see true innovation in MMORPGs until we see more middleware, to greatly lessen the time it takes to design. Maybe what MMORPG players really need more than anything is better MMORPG middleware.