I'd like to nominate Excel Saga and Cromartie High School.
Excel Saga is about a group (of 3 people) who are trying to achieve world domination. The main character is Excel an ULTRA hyperactive minion of Illpalazzo, the leader of the group who try to take over the world. She completely fails almost every assignment she ever has to do. Throw in some incredibly cute evil Aliens, dog eating, random death and destruction, Pedro the dead foreign construction worker, Nabeshin and... well. Watch for yourself.
Cromartie High School is about a dude who gets transferred to THE most delinquent High School in Japan. An example of the students who attend there:
Freddie Mercury, Gorilla (yes, a gorilla), Mechazawa (a robot who doesn't know he's a robot). They're all incredibly dumb and have many random adventures.