Neutering is generally recommended for all cats and dogs.
Not only does it prevent unwanted litters, but it also prevents some nasty cancers (testicular, ovarian, mammary) and complications such as prostate problems and pyometras (infection of the womb which is potentially life-threatening). If performed at an early age it can also help with behaviour issues.
The best age to neuter depends upon the breed of dog, the vet doing the procedure and clinic protocol. Generally, cats are neutered at approximately 5 months of age. Small & toy breed dogs will also ideally be neutered at about 5-6 months, while large and giant breeds tend to be neutered at 9-12 months of age.
Pets can put on weight once they have been neutered, so you will need to exercise them regularly and monitor their weight. Also, changes in the pet's coat may occur; their coat might become more fluffy and puppy-like. Some breeds are more prone to this than others, such as Setters and Spaniels. Finally, female bitches have a higher incidence in urinary incontinence later in life, but this is easily controlled with medication.
All things considered, the pros definitely outweigh the cons when it comes to neutering.