Yeah, it's a big dorky thing for dorks, but there's actually some really cool stuff, too. Don't be put off by all the tentacle rape, maid and/or harem fantasy crap and the creepy stuff that's like Bewitched without the excuse.
Pretty much anything by GAINAX, including Neon Genesis Evangelion, His And Her Circumstances, FLCL (a/k/a Fooly Cooly)
Serial Experiments Lain
ANYTHING by Hayao Miyazaki or Studio Ghibli, but you so shouldn't need me to tell you to see My Neighbor Totoro or Spirited Away or Howl's Moving Castle or basically any of the rest of them because they are so utterly beautiful they will melt your brain with happiness.
Full Metal Alchemist
The Top Stuff was by Rev. Sung Myung Me, this is Capt. Zeston Norelco's add-on
this addition is by vkeios. (I'm a complete dork for anime, so I had to add some)
"Azumanga Daioh" Its about high school girls in school. Its the Seinfield of anime.
Elfen Lied Disturbing thing about an evolution of humans. Nothing good happens to any of the characters in it ever.
Pani Poni Dash Little girl who is high school teacher. Random like FLCL, but a lot of jokes are based on anonymous image board humor.
Welcome to the NHK A show about a hikikomori and the religious (might be Jehovah's Witness) girl who tries to cure him.