I've only read (more and less) about dozen mangas and seen same amount of animes, plus about another dozen or two anime movies (individual or series-related). I haven't yet found any clear favorites.
Favorite manga might be Hellsing or Death Note; haven't seen the animes (or other versions). A different choice would be K-On!, a cute strip comic (also haven't seen the anime, would really like to) or Ranma ½ (funniest one).
Anime is even harder to say. There's the Studio Ghibli films. Neon Genesis Evangelion is a classic series. Couple OVAs come to mind: Battle Angel Alita (the film will have hard time matching this two-part anime) and second part of ca. 1990 Devilman OVA (Demonbird) has special meaning for me as first piece of anime I bought - and still possibly the best because it has so much cool action.
Separately I must mention dog manga/anime Silver Fang, being about only series I've both read and seen (aside missing couple episodes).