I've only seen three anime shows: Sailor Moon, the Dragonball trilogy, and Pokemon.
All three are extremely repetitive (but isn't that some sort of cutural norm for the Japanese?), but they all have their interesting characters. I have a tendency to like the antagonists, specifically the first ones that appear on the show. For a while I was re-watching Sailor Moon, both subbed and dubbed, up until Jedite was crystalized...I kind of liked it - I thought Jedite was a neat character. Getting run over by a jet only left him limping.
As for Dragonball, I only (if accidentally) managed to catch any of the episodes having to do with the Red Ribbon Army, whether it be the army itself, Dr. Gero and his androids, or Super 17.
As for Pokemon...well, I'm still watching that - the newest season, Diamond and Pearl, is completely unpredicatable and the writers are practically breaking traditions at nearly every turn! The Characters-of-the-Day and all the Pokemon actually have personalities, plus there are formidable Hunters like J, who turns Pokemon into gold and sells them for profit (she managed to capture Ash's Pikachu, Team Rocket's Meowth, an Absol and a Gardevior in less than 10 minutes), and real jerks like Paul (watch Diamond/Pearl season episode 51: "Chimchar vs. Zangoose! Battle of Fate!" to see how harsh with training he can be).
As for movies, so far I have seen Spirited Away, Princess Mononoke, Nausicaa, Totoro, Kiki's Delivery Service, and Howl's Moving Castle...I might have missed a few, though...