Study: REM sleep and tears...

This is kind of an interesting theory - basically that during REM sleep the reason we blink so much is to keep the eye surface wet.

REM Sleep: Tear Secretion and Dreams.
Murube J.
Ocul Surf. 2008 Jan;6(1):2-8.

ABSTRACT Although a number of hypotheses exist to explain the reasons for the rapid eye movement (REM) phase of sleep, the physical movements themselves have not been explained or interpreted in the literature. The author theorizes that REM during sleep serves not only to increase the lacrimal secretion and to humidify and lubricate the ocular surface, but also to redistribute the secretion on the ocular surface and to inform the conjunctiva-associated lymphoid tissue (CALT) system. He hypothesizes that when eyes move in REM periods to humidify the ocular surface, they indirectly release phenomena of the visual activity, producing dreams.