Don't know what's eating them but you don't want a ripe cucumber. You pick cucumbers while they are still immature. If they were ripe, they would be yellow and have hard seeds. However, when you pick them is totally up to you. When you feel like they've reached a large enough size to eat them, pick 'em. With time you'll find out the lenght and thickness that you enjoy (it's a personal preference really). The one in the picture looks like a good size to me, I'd pick it.

Rodney

Thanks Theforgottenone

suspect rats. About harvesting: you can do it at any stage. Cukes and squash need not to mature. Maturing result in hardening the seeds inside and less desirable.