If you venture to a local pond/lake and observe the mallards and black ducks, some of them have one of their eyes open while sleeping because they can keep half of their brain awake. I just happened to notice it while on a daily walk and had to go look it up afterwards. Ducks also make outrageously loud quacks when alarmed (sounding similar to a single person laughing too hard at an unfunny joke). Made me jump more than once when walking after dark.
Not all of them will always sleep with one eye open, but at least a few in a group will in order to keep watch from coyotes, birds of prey and stray cats when they're not in the water.
http://en.wikipedia.org/wiki/Unihemispheric_slow-wave_sleep