Most of the time i either read the manga or watch the anime, exactly because there can be huge differences, so the only ones i know about on this list are Elfen Lied and FSN.
Elfen lied's manga's story is about 3 times as long as the anime, but its finished. It seemed like both are good, but the manga has a lot less of those small mistakes, and lot less blood too actually.
Of Fate/Stay Night, like genji, i'd also rather recommend the visual novel rather than the manga. The anime was a little bit too hurried, i guess even 26 episodes were too short for this story, and while the manga is a lot more detailed, it follows a different storyline. On the positive side, this time unlike the other mentioned mangas/animes, these are both original storylines, so its worth reading, but the visual novel is just so much better than the two of them together.
Something must be wrong with me. I'm giving advices to someone i should kill.