I'd also recommend Final Fantasy XI, as a healer.
Progress through the game as a healing class isn't nearly as difficult as it may be with another, because they're very desirable; and play a crucial role in the game's lengthy grind.
It's a very 'civilized' MMORPG with a great community, and endgame encounters are very organized, where all the basic class archetypes play an equal role in taking down a boss.
Overall, you've likely heard that it's a more difficult game, when compared to others, such as WoW (though, some of endgame is significantly easier-- or, at least, "well-balanced")... I think it's definitely worth looking into, and can be a very fun, rewarding experience.
Being a long-time (since '03) player, I'm always looking to help newbies out in FFXI, so if you decide to play, drop me a PM.