Does pink eye cause blindness?

Pink eye is a "cold" No, pink eye is a viral infection of the conjunctiva that will run a typical course in about a week, just like the common cold. There can be temporary vision disturbances in some cases but there is no risk of permanent vision loss or blindness.
No but... The bacterial eye infection called trachoma, which is not seen much in the usa, can start initially as a conjunctivitis and slowly progress to blindness.

Related Questions

My newborn has a gunky eye. The GP took a swab to see if it's conjunctivitis or blocked tear duct, if conjunctivitis can that cause blindness?

Unlikely. You have done the right thing by having your child's eye looked at. You can keep it clean with use of warm washcloths until the results come in. Conjunctivitis is an infection of the outside lining of the eye - occasionally bacterial and sometimes viral. Blindness is remotely possible but very rare except with infections that occur during birth now routinely prevented. Your baby should do well. Read more...