I like anime a lot. If you can find a good show with interesting art, compelling characters, and an involving story you should give it a try regardless of the genre. I just find that's the case with most animes.
Some of my favorite titles are Chobits, Death Note, Wolf's Rain (till the end, anyway) and D.N. Angel.
That said, my personal guilty pleasures are Love Hina and Digimon Frontier.... *is ashamed.*
Wakikifudge said:
The wacky hairstyles, the giant swords, the men that look like women, the way people suddenly get giant heads when they yell at people....my reasons for hating it go on and on.
Hmm... perhaps you've been looking at the wrong genres of Anime. I would recommend Slice of Life style animes, or perhaps action or period action animes. Baccano! and Welcome to the NHK are some pretty good ones.
Little warning on the latter, if you decide to watch it, the style of humor is pitch black, no cream or sugar, and all the characters are horribly messed up, but it's a pretty damn good show (the dub is better)
EDIT: ANYTHING by Hayao Miyazaki (particularly Howl's Moving Castle... if only to hear Christian Bale do his silly Batman voice in a different context X3) is really good too.