I don't think there's anyone who's heard of anime at this point that hasn't heard of Fullmetal Alchemist. With good reason -- this first series is excellent, with high-quality production, an excellent mix of humor and deeper meaning, and an ever more engrossing and intriguing plot.
For those not already aware (anyone?), the premise of Fullmetal Alchemist is that Edward and Alphonse Elric are alchemists who, in a gruesome mistake, attempt to use forbidden alchemical techniques to resurrect their dead mother. The experiment goes badly, Al's soul is attached to and animates a suit of armor, and Ed loses an arm and a leg, literally, to be replaced by prosthetic automail. Ed becomes a state alchemist and the two go in search of the philosopher's stone in the hope of restoring their bodies and making things right again.
The above plot summary, while technically accurate, is also misleading by itself as to the underlying tone of Fullmetal Alchemist. Perhaps it would help if I mentioned that the state that the Elrics work for is run by a Fuhrer King Bradly, there are homunculus that want to kill oodles of people, and someone powerful is after revenge against the state alchemists.