the first Fullmetal Alchemist anime series changed the story line to something completely different because it had caught up to the manga. so they decided to make something up entirely different. that goes the same for the movie that followed up, "the conquerer of Shamballa".
the new FMA:Brotherhood completely follows the manga to the end. in fact, the broadcasting of the final episode of that series was only a few weeks after the final manga chapter was printed!
one series no one has mentioned was
Tengen Toppan Gurren Lagaan
a great series by Gainax.
I am also a big One Piece fan myself. I discovered this anime on a whim when I used to buy pirated Anime DVDs from HK at the small shady DVD shops around Richmond. at first, the series seemed somewhat childish but the action was always there. now, the storylines and characters have really blossomed into something really
great, and it definitely shows why it is immensely popular in Japan.
edit: oh yeah, and since this is REVscene, we all have to suggest
Initial D!