Have you guys ever heard about meibomian glands? They are a special kind of sebaceous gland that exist on the inside of your eyelids. Though they are similar in structure to sudoriferous glands, they function a little differently -- namely, to keep the eye's supply of meibum, a fatty substance going to keep the eye from drying out.
This is also why closed eyes are more or less watertight, and you don't continuously have tears spilling down your cheeks.
I just recently researched this for a class on glands and hormones, and as soon as I read this article about sudoriferous glands I just had to whip out my new knowledge! How cool is the human body that it has so many different kinds of glands that all do different things?