I hate a lot of stuff, however both Full Metal Alchemist and Cowboy Bebop are excellent, they both have endings and good villains. There is nothing worse than a shonen manga like Naruto, Bleach or One Piece that is never going to end.
That said, I love One Piece it is my all time favorite, but I wouldn't recommend it for the reason I won't recommend Bleach or Naruto (and I read both). Oh and despite the hype Naruto is going straight in the shitter, even if you ignore the filler episodes that the series is taking over a year to do the manga is getting less and less entertaining.
Another good series is Gantz, it suffers from the lack of decent villains and the monster of the week-ness but the characters are very likeable plus no one is sacrosanct, no one is safe and that fear that your favorite characters are going to die makes the show/manga very sweet.