There is a great variety of material available that captures the aspects of Anima:
1. Witch Hunter Robin (Anime); a lot more hi-tech than Anima but captures the duality of the Inquisition in hunting Witches (Humans with psychic abilities) using Hunters (Humans also with psychic abilities). It also has the underlying story of an ancient race that ruled humanity (Witches). All in all, fun to watch.
2. Princess Mononoke (Movie); awesome movie that captures the advent of technology present in Anima with the arival of blackpowder weapons in a feudal Japanese setting. It is definitely more fantasy set then Anima but it shows Humans and the way they interact with the Spirit world, (aka. Fear, revulsion, outright hostility, etc.)
3.As noted above, the Final Fantasy game series is great in that it combines epic storylines, heroes with incredible abilities and over the top action sequences. Plus. a majority of the games have some dealing with a Spirit-world or dimension parallel to that which is normally percieved.(Much like Hell in Anima) And most importantly, Big swords being used one-handed!!! (Strength 10 is awesome!!)
I look forward to finding everything else that has been posted here, it all sounds very interesting. Thanks for reading!!