We don't do them routinely, but if a kid's eye is gunky we'll culture it. You get some naaasty stuff growing in eyes.
On an even grosser note, today I had a 2 day old baby whose right eye was stuck closed with vernix!

She'd gone straight from the DR to the OR for a gastroschisis repair, so she never got a bath or anything. I really hate combing days old blood and dried vernix out of a baby's hair. Hate it a lot.