Many people do not realize that unlike female dogs, who experience a heat cycle once every 6 months, female cats go into a heat cycle every 17 days. They also differ from dogs in ovulation. Whereas it is important to know where in the cycle a dog is to produce the best chance at pregnancy, cats are induced ovulators. This means they release their eggs at the time of intercourse. As a result, female cats can have multiple fathers for a single litter. (Ever wonder why a black cat may have a litter of 6 to 8 kittens, some black, some orange, some white, some grey? Now you know. They all have the same mother of course, but each could potentially have a different father.)
A cat in heat will attract intact males from all over the neighborhood, right to your door. These tomcats will yowl and fight over the female. Again, unlike a dog, a cat can get pregnant just one month after having a litter. So an outdoor cat will keep having litters that will need homes. Even if your cat is always kept indoors, she will release pheromones that we can not smell, but that will draw tomcats to doorways and windows around your home. She will see or sense the males and respond by crying and yowling. The toms will respond in kind and may start spraying around the house to mark territory.
Female dogs and cats share many benefits from being spayed, other than the lack of heat cycles mentioned above. Spaying before the first heat cycle can potentially eliminate the risk of mammary (breast) cancer. The risk is significantly reduced, but not eliminated altogether, if spayed after the first heat cycle. Unspayed females of both species can develop a pyometra, which is a life-threatening uterine infection, often requiring emergency surgery. Intact females run the risk of developing cystic ovaries and having false pregnancies, both of which may result in wildly fluctuating hormone imbalances. Finally, complications can arise in any pregnancy that could leave you faced with an expensive emergency C-section.
For males the issues are a bit different, but just as worrisome. An intact tomcat will roam an entire neighborhood looking for a female in heat. He will often fight mercilessly with other toms over first right to the female, resulting in costly vet bills for bite-wound abscesses. Intact tomcats spray to mark territory both inside and outside the home. Spraying and other forms of feline urinary marking are greatly reduced by neutering early.
Unneutered male dogs may also fight and become aggressive. They have been known to dig under fences and jump through windows (yes, even closed windows) to get at an intact female. Intact male dogs can smell a female in heat up to three miles away. It is believed a tomcat can smell a female in heat over a mile away.
In either case, that is quite a distance to travel with a mind focused on only one thing. The risk of severe injury, especially being hit by a car, is very high among intact males of both species. Intact females may also be enticed to wander away from home looking for a mate. Although there are no definitive numbers, Animal Emergency Hospitals and Animal Shelters list statistics of 80 to 95% of all hit-by-car cases are from pets that have not been spayed or neutered.