The Lord of the Rings Online MMORPG is currently undergoing Beta testing. It does have a monthly fee (as of yet undetermined), but the graphics seem more detailed than Warcraft and if the fee is less and the creators more interested in player input (something Warcraft fans don't appreciate about Blizzard), WoW has some serious competition on its hands.
Drawbacks include a seeming lack of pvp, since players have only 4 races to choose from: Humans, Elves, Hobbits, and Dwarfs. But new, interesting classes may tempt players: champion (offensive warrior), guardian (defensive/tank warrior), captain (inspirational warrior), burglar (rogue), hunter (no-pet hunter), minstrel (story-teller, support class, maybe similar to priest), lore-master (knowledge keeper, support class, maybe similar to priest).
All in all, I think the lack of world pvp will hurt the game's chances to lure more Warcraft players away, but the Warcraft players who play an elf because it's like The Lord of the Rings, or who liked Warcraft for having the best graphics around, will be weak enough to leave. Still, if LOTRO doesn't live up to Tolkien's legacy and its own hype, we'll probably see players leaving to try the game and then a slightly smaller number of players coming back.