Are animals that are known to mate for life known to cheat?

This question came to me when I wondered if primates do the same thing humans do, that is, check out the opposite sex even if they're in a long-term relationship. Do monkeys "read the menu, but not order anything?" Furthermore, do monkeys (or any other animal) break the bonds of animal (for lack of a better word) matrimony?

The next question this raised in me is that how are "animals that mate for life" classified? If 75% of carrier pigeons mate for life, but 25% fuck around like Kim Kardashian, does that qualify the species or is it an all or nothing distinction?