A cat's eyes may be watery and runny for a variety of reasons, including a clogged tear duct or irritation from debris. One cause to rule out is crying, because cats do not cry the same way people do.
If a cat's watery eyes are accompanied by a thick yellowish discharge it can be a sign of a feline viral respiratory illness, according to WebMD. An insufficient tear-duct system can also put the cat at risk for chronic infections in the eyes. A cat with persistent tearing or watery eyes should be seen by a vet to receive proper treatment and to determine the exact cause.