Perfect Blue was completely amazing. It got me so into it at the end that I wasn't sure what was real, or if I was going crazy.
Elfen Lied gets maaaajor points from me for gore and amputation galore.
Paprika, like Chrono said, was spectacular. I have never been so afraid of a refrigerator. Watch the movie and I am sure you will know what I mean. The ending was a tear jerker for me. Freaky and cute and heartfelt all at once.
A lot of people said they like Gantz, and I couldn't agree more. At first I couldn't get into it because it was all about a guy getting boners in public. Sorry, but I can't relate. But, I stuck through it and watched both seasons in about a week. By the end of the second season I was so depressed and scared. The end of the anime is a little bit lame. HOWEVER, the manga is ongoing and really adds to the series. If you want to see the only survivor continue his journey read it, it's free online if you know how to use google.
If anyone wants good guro manga read Jinji Ito's stuff. He wrote Tomei, and Uzumaki. The Battle Royale manga is really intense if you want to go there too.