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It is beneficial for both the animals ane their owners to have both male and female dogs neutered.

If bitches are spayed early, they are far less likely to develop life threatening mammary gland cancer and uterine infections, both of which are more common later in life, but can be seen at any age. Spaying of the bitch also eliminates her biyearly cycling and therefore her drive to run away from home. The spaying surgery does not cause obesity, but it is important to realize that spayed bitches have reduced caloric requirements and therefore should receive smaller meals.

Queens are spayed to prevent repeated pregnancies and to decrease their tendency to stray and contract various diseases from other cats on the street.

Castration of male dogs helps reduce the likelihood of most prostatic diseases as well as other health problems seen more often in intact male dogs (ie perianal hernia, perianal adenoma tumors etc). The surgery also reduces straying, interdog aggression, dominance aggression, wetting indoors and antisocial mating behavior.

Tom cats should always be castrated. 
The castration of male cats is one of the simplest operations that we perform and has great benefits for both the owner and the cat. All cats are extremely territorial; uncastrated male cats have a strong drive to trespass in other cat's territory in search of females.
This drive results in high tendency for fighting, wounding , straying or an often fatal traffic accident. To decrease the frequency of trips to the vet for patching - up and to prolong the life of your male cat, he should be neutered.
Neutering also prevents indoor marking behavior with strong smelling urine. Castration of the male cat turns him into a home loving boy and a much better pet.

Preferred times of neutering
Cats/dogs, male and female : at 6 months of age - before 1st heat cycle / onset of puberty.