Umineko No Naku Koro Ni (When The Seagulls Cry)
I've only just started watching this anime, and it's already one of my favorites. The "Intense Moments" may be a bit unbearable at first, but once you get into the story, you'll hardly notice them anymore. After the second or third episode you know that this anime isn't playing around.
Rated: 17+ for violence and profanity