Personally, I play WoW for a few reasons:
1. It's fun. Beating up bad guys, hanging with other people, dressing up my toon with awesome gear. The story is interesting, and sometimes I like to read into the lore (Warcraft manga anyone?). The graphics aren't too great, but then my computer is crap (getting a Macbook soon, so this should be resolved). I really like the music in the game, although I hear some people mute it and play their own, which is fine if you aren't interested in immersing yourself in the experience.
2. What other games are there? I've played many games in my life, but not many of them can get me to come back like WoW can. Some people think this is a bad thing, but to be honest, if a game can't keep you interested, then the developer is going to either go out of business, they'll shut down the game for good, or they need to make more games.
3. Of course, what post about why people play Warcraft would be complete without asking which faction people side with? Personally, I don't take sides. When I started playing WoW I played for the race/species. Draenei to start with, paladin of course (yes I've tried other classes, no I didn't like them). I just finished levelling my sin'dorei (blood elf for people who only speak the common tounge). I have a tauren warrior, but I don't play him, and when the next expansion comes out I'll be trying out a worgen hunter.
So... let us know what your reasons for playing Warcraft are. Comments can be as long or short as you like, just make them sensible and coherent please.