I just finished watching the anime series Neon Genesis Evangelion. To anybody remotely interested in Anime I'd really REALLY recommend you check it out. It's considered by many to be a ground breaking in Japanese anime. The author of the series was a suicidal manic depressive while he wrote it so it expresses alot of this personal problems and feelings through it's story.
One of the types of things that makes Japanese anime generally stick out from American cartoons is that, where as American cartoons are usually meant to be light entertainment many Japanese anime are very serious with very deep topics. Not all of them but even the fluffier ones often deal with much more mature topics then found in American cartoons.
I will warn you that the ending of the series is generally disliked. There are 26 episodes each about 22 minutes long. The original series stopped at episode 24. The Japanese fans were so upset that 2 more episodes were made to explain a little more. I'm not sure the series is better with or without the extra last 2 episodes.
But, the trip to those last 2 episodes are pretty darn entertaining. I found that after the first few episodes I was dying to watch the next and the next.
I watched in Japanese though which means I didn't get all the same meaning out of it as if I had had subtiles or English. I'd really recommmend you go out and rent them. I think if you do you'll find you get hooked after a few episodes. I think I'd recommend it with subtitles if you can find it (probably you can't though unless you read the DVDs). The reason is it's hard for me to imagine that the dubbed version could have as perfect screams of rage and terror that the main character often needs to express.
If that last sentence scares you off let me explain. *spoiler warning* The series is about future world where mysterious forces are trying to destroy earth and/or part of Japan. Japan has a high tech defense system based on giant robots that are controlled by getting inside a special capsule (think torpedo) which is then filled with a fluid and inserted into the robot. Control is by direct mind link (and a few handles). Anyway, in the first episode the main character is put in one of the robots (which can only mind sync with 14 year old kids) and he doesn't really want to be there. He nearly gets killed and you don't see the battle. The next episode he wakes up in the hospital with no memory of what happened or how he survived. Through flashbacks you find out that when he was within an inch of dying he went beserker (mad with rage) and the screams from the voice actor for those scenes fit perfectly. I suspect they don't on the dubbed version.