What other words/terms are used to mean 'sleep'?

The actual medical term is rheum (which applies to nose and mouth excretions that occur during sleep, as well).

"Sleep" is what I grew up saying, but if Discovery Magazine is any guide, kids now say "crusties" as well. (The article also describes the organ responsible, if you're curious.)

Sleep always kind of creeped me out for being vague (and euphemisms generally unsettled me, making me feel like the actual thing was unspeakable), and "crusties" and "eye boogers" seem too childish now.

I think eye gunk is clear and not cloyingly juvenile; it gets my vote.

I knew it as sleepy dust when I was a child.