I have watched quite a lot of anime and read quite a bit of manga, but I can't say I'm a fan, no more then I'm a fan of american TV serials. It's just another potential avenue to waste time in, sometimes memorable, often tripe.
There are a few series that I really like, but they hardly make a dent in the absolute crap that gets pumped out.
Some of my favourites? Most of these are commonly, highly, regarded, some are just personal favourites for no particular reason:
*Evangelion, the old series and the rebooted movies.
*Dragon Ball and Dragon Ball Z for nostalgia reasons, a lot of the new series do what DBZ did better, but I grew up with DB and DBZ
*Full Metal Alchemist. The original Anime that deviates from the Mangas though, don't know why I prefer it from the original source.
*One Piece to a point, I haven't gotten back into it in a few years now, but I loved it when I had time to follow it.
*Ghost in the Shell 2nd gig. I much prefer it over Stand Alone Complex.
*Ghost in the Shell Movies, original and Innocence (the STC movie wasn't great)
*Paprika, only watched this recently, was pretty good.
*Red Line... pure style over substance, but massively entertaining.
*Clannad... for all the painfully childish romances, the series grew on me and the 2nd season was a real whopper.
*Most of Ghibli stuff, but Totoro, Mononoke, Porco Roso, Grave of the Fireflies, Moving Castle and Spirited Away are my personal picks.
I've watched a lot of other series and movies, and while I didn't dislike them, none of them really make me invested in Anime.
So no, not a fan, just have a casual interest.