In general, we recommend you spay or neuter your pets if they are not intended for breeding. Pets should have finished their puppy/kitten vaccines before scheduling surgery. We generally like pets to be 6 months old but this can vary depending on the pet.
The two main reasons to spay or neuter is to avoid overpopulation of animals, and to reduce the risk of certain diseases. For example in tact males have an increased risk of prostate and testicular cancer. In tact females are at risk for Pyometra, an infection of the uterus that if left untreated can be deadly.
In addition, they are more at risk for breast cancer, ovarian and uterine cancer. Some common myths you may have heard are that spaying and neutering causes laziness, reduced protective instincts, delayed maturity or alter their personality.