Excel Saga

Some anime series fall into the venerable category of "strange." This one is one of the strangest of the strange. You have a male leader, a female who will do anything for him but is fairly normal otherwise, and a female who will do anything for him but has a rather bad habit of dying again and again and again.

The series is really quite funny.

By the way, the dog (yes, it looks like a cat but it's a dog) on top of her head is an "emergency food supply."