Started watching anime in the early 90s because of Dragonball. That's right, for better or worse, I'll always be a DB kid, and there will always be a little place in my heart for it. But as with anyone, you develop different tastes over the years, and the usual shounen fare does not interest me anymore.
Nowadays I prefer more of the slower, story/character driven, mature type of anime. Monster, Kino's Journey, Daughter of Twenty Faces, etc. come to mind. Epic periodic/fantasy pieces sway me. The occassional adventure, drama, occult , slice of life and comedy, all when done right, round out my interests. I'm also a big anime film buff. Generally, I'd sit down and watch a film over a series no matter how bad. To no surprise, Miyazaki and Kon are my favorite directors.
Notes: I don't rate anime that's been dropped or stalled; only those that have been completed*. Therefore, my ratings are generally high. Any anime I tend to finish have usually been good enough for me to watch all the way through. And most of the time, any anime teetering below par doesn't get the opportunity to waste my time with a full watch through, and either gets stalled or dropped completely. Makes sense, right?
*One Piece is the lone exception. Considering that it's poised to last a century, rating what I have seen (up to date) seems fair.