I've noticed there seem to be quite a few anime watchers on the forums, so I figured I (being a big geek) would check to see what everyone likes! Post as many as you want, and why you like them. It doesn't have to be a currently running anime either.
To get things started, here are 5 of my mainstream (released in America, though note I don't necessarily like the dubs) favorites:
Yu Yu Hakusho - I really liked the concept of this anime, and although it wasn't quite as good after the Dark Tournament it had some great characters and great fights.
Cowboy Bebop - I loved the art style, the music, and even *gasp* the dub voice acting. The anime was moody and thoughtful, but knew how to be funny too. This will always have a spot among my favorites.
Fullmetal Alchemist - Another anime who's concept really grabbed me from the getgo. The plot was great, leading the viewer to one surprise after another. It also is one of the few animes to include a movie as an actual canon part of the plot, and the movie finished the series perfectly.
Robotech Macross - I have so many great childhood memories of this show. It was touching, had great music, and some really epic scenes. The show was way ahead of it's time and set standards for all future anime.
One Piece - a fresh art style, great unique personalities, plenty of character deveopment, lots of humor, and a break away from many anime norms help push this popular anime (in Japan anyway) into my list. It's only issue is that it's plot is a bit cyclical. The anime is often underrated in America due to a horrific mutilation of the show's plot, humor, and violence by 4kids animation.