As it stands now, World of Warcraft is the top western market MMO. Best guesses are that between North America and Europe it has around 4 million subs. It features classes, levels, quest based progression, and relatively restricted character customization compared to classless MMOs. These features are also found in Lord of the Rings Online, Runes of Magic, Everquest II, Age of Conan, Warhammer Online and a screaming ton of other MMOs that are relatively sucesful. Between them (along with WoW), these class/ level/ quest based MMOs serve the bulk of the western MMO market.
This is hardly the only possible way to structure an MMO. EVE online is often held up as a counter example by hardcore/ oldschool MMO enthusiasts (and crazy hobos). There are no classes, what you can do is limited purely by your skills and what ship you can afford. You are free to develop whatever skills interest you. You don't develop skills by crafting, killing fools, or standing in line at the bank. Instead, you decide what skills you'd like to work on and they start ticking up whether you are online or offline (as long as you pay a sub fee). There are a ton of other things that set EVE apart from typical MMOs. The entire game takes place on a single server, the crafting system makes the crafting in most MMOs look utterly shallow, and my grandmother doesn't bitch me out if my casting rotation isn't what is should be.
Can a non WoW-ish MMO prosper? Seemingly so. EVE now ranks a among the top ten western market MMOs. Likely among the top five, but the list gets very fuzzy past WoW (the rank depends a lot on who you ask). If the learning curve to even get started in EVE wasn't so insane, it might be able pass the 500K mark that most non-WoW MMOs seem unable to crack (in the western market). If any non-level/ quest based MMOs passed that mark, it would in turn signal the folks with cash to fund development that new MMOs don't have to be WoW/ EQ clones to prosper.
Sadly, I doubt that will happen in the next few years. I seriously doubt it will happen for EVE, DF, UO, or any other current sandbox MMO. None of them is particularly easy for a new user to pick up and play. Sure, they are incredibly deep and rewarding once you get past the initial hump. But the average western gamer doesn't like humps. I think EVE is roughly as successful as the current generation of sandbox MMOs has the potential to be.
I predict, instead, that Bioware's new MMO will be the next one to crack the 500K mark here in the West. It will feature classes, levels, and fairly linear gameplay. The wild success of the game will be attributed to its emphasis on story and solid professional writing. This will be an accurate assessment, as far as it goes. LoTRO, Guild Wars, and the more recent content from Blizzard have pushed forward the envelope on presenting compelling stories in MMOs. However, Bioware will likely take this to an extreme that will make NCsoft, Blizzard, and Turbine look like rank amateurs. The new MMO from Bioware will allow us to experience several movie's worth of story, all while chilling out in our undies in front of a PC. We will all be astounded, hail Bioware as heros, and perhaps get tattoos. "This is what has been missing!!!" we will all proclaim.
All the while, the concept of a sandboxy MMO with a big budget and a learning curve less harsh than getting afflicted with boils by Satan will remain untested. EVE, Ultima Online, Darkness Falls, Saga of Ryzom, and the editor that comes with Neverwinter Nights simply aren't new user friendly enough to give us a fair test. After watching the market fall in love with yet another class/ level/ quest based MMO, it will likely be a long time before we get a more openly designed MMO with a decent budget behind it.