Cancer
Most studies have shown that the relative risk (compared to intact dogs), of mammary cancer increases after each heat cycle. For example, the risk of mammary cancer in a dog spayed before the first heat is 0.05% but becomes 100% after the 3rd heat. In cats, a 2006 study showed a 91% reduction in mammary cancer risk in cats spayed before 6 months and an 86% reduction when spayed before 1 year of age. Now there are questions about the methodology of some of the older studies, but it does appear that hormones play a role in the development of mammary cancer, the lower those hormones are, the less likely a pet is to develop mammary cancer. What about other types of cancer? Well, the studies there show mixed information, for example, the risk of osteosarcoma or bone cancer is about 3 times higher in both males and females, and the risk of mast cell tumors is 4 times greater in spayed females. There is currently not very much data on cat cancer risks.
Other health concerns
We know that neutered male dogs have a lower risk of perineal hernia, benign prostatic disease, perianal adenomas, and male-on-male aggression. Neutered male dogs, however, have a high rate of obesity, cruciate injuries (knee), diabetes, and hip dysplasia. Spayed female dogs have a decreased risk of pyometra (uterine infection) and ovarian tumors. Increased risks for female dogs include obesity, cruciate injuries, and a 5% risk of urinary incontinence. Now cats are a different story. We know that female spayed cats have a lower risk of pyometra but an increased risk of obesity and diabetes. Male neutered cats have a lower risk of roaming, fighting, and spraying in the house, but an increased risk of obesity and lower urinary tract disease.
All of these studies, however, have some flaws. While a connection may be present, there is not enough evidence to conclude there is a causation; one may not cause the other. The studies that have been done are exclusively large breed dogs, such as Rottweilers and Labradors. These results may not extend to dogs of different sizes, in fact, one study found different results in pointers as compared to retrievers, which are similar-sized dogs.
Broad recommendations are difficult to make and are best made for an individual pet with input from our medical team, however as a general rule:
Male cats
Neutering prevents behavioral issues making neutered male cats better pets. There are currently no major known health downsides to neutering cats.
Female cats
Cats should be spayed before or around 5 months of age to prevent mammary cancer which is highly fatal. Spaying also eliminates the risk of pyometra. And like the male cat, there are no major known health downsides to spaying.