What persistent multiplayer online games are there that don't require a lot of grinding to gain levels or unlock the really fun content?
Bonus points to a "flat" skill tree. In other words it's not about how long you've been playing the game, it's how you make use of your options, of which there should be a lot.
World of Warcraft is the largest scale deployment of its kind and I feel over time the leadership over at Blizzard whom produce the game have learned that grind is not fun and have reduced this drastically over the years of this games evolution so it would get my vote.
How about a basic browser game?
Dragon's Call is a good one, although it is now limited to just three classes, it still is a good MMO IMHO(you can do it in the office!)
I would have to recommend
EVE
[1].
It's the only MMO I play because there's no levelling and nothing really needs to be "unlocked".
There's a bit of 'grinding' if you just want to run missions to increase standings, but it's not bad: some people grind missions for fun and profit!