Is it a good idea to let my pet have at least one litter?

No, there is no advantage to letting your pet have a litter. There are however plenty of advantages to having you pet spayed or neutered. These advantages include decreasing the chances of mammary tumours later in life, eliminating the possibility of uterine infections, decreased urine marking behaviour. Spaying and neutering pets also helps to reduce overpopulation of cats and dogs.