I played it during Vanilla and that started up again with the Burning Crusade. I originally started it with my brother and I loved it. It was new and interesting, my first mmo and pretty standard fare for an RPG. Burning Crusade added some new things and fixed a bit, but being a student I really didn't have time for it anymore. My brother still plays Wrath and they've streamlined a lot of stuff and made it more casual friendly, although like all MMOs, it's a total time sink and grind. Yea, the game is getting better and 1-60 lvling is supposed to be streamlined in Cataclysm. But unless you're in a raiding guild, I don't really see the point in playing the game seeing as you'll see all the content once you hit max level and while you're leveling the game isn't anything special that you couldn't experience with any other game.
Not too mention that story wise, compared to most traditional games, just isn't there. There really isn't any sort of overarching story or narrative. Just a bunch of mini-stories that start and end in each new zone. Don't get me wrong, the game is pretty fun, but if you've got the money to blow and already have a steady internet connection you'd probably get more fun out of a solid online FPS.
Although, if for some reason you HAVE to play an MMO, I'd play WoW as it pretty much outshines all the others out there right now and is pretty casual friendly.