Sleeping Dolphin

Dolphins sleep with one eye open and only one part of their brain slowed down at a time. They either float at the surface of the water or stay at the bottom.

Here are the links for the references of this fact:

http://en.wikipedia.org/wiki/Dolphin#Sleeping

http://www.randomfacts.com.au/rf/random_facts/random_animal_facts.html

And here is a video of a dolphin sleeping:

http://www.youtube.com/watch?v=1ZSzI5mHwS8