At one time, the wait time was 6 months to have a puppy fixed. We bought an English Setter and the vet recommended having her fixed at 3 months which we did. The vet said there are health advantages to having them fixed younger versus waiting for 6 months or older.
Our vet will neuter/spay after 12 weeks. The biggest advantage to neutering before the 1st heat cycle is that the cat or dog will likely never get cancers of the reproductive organs, and a female will probably never get breast cancer.