Spay and neuter your pets. You've heard that a million times or more. Many people do it simply because it's what the vet recommends. But do you really know why? And if you chose not to, do you really understand the risks you're taking? I'll try and help. Because reproductive issues are the least compelling reasons to have the surgery done.
First let me make one thing clear. Dogs and cats have no awareness of their own sexuality. They don't have a conscious perception of what those reproductive organs are really for. They don't judge themselves by whether or not they have testicles or ovaries. I want this to be known, because a large reason why many men oppose neutering is because they don't want to "take away his manhood." I hate to break it to you guys, but your dog or cat doesn't know what his "manhood" is, and isn't aware of what has happened when they're gone.
Neutering helps lower the risks of behavioral problems in males. Intact males are more likely to "mount" inappropriately, urinate to mark their behavior (including inside the house), roam, be territorial, and be aggressive. Neutering them before puberty (7-9 months old) dramatically lowers risks of these unwanted behaviors. Neutering also eliminates the risk of testicular cancer and lowers the risk of certain kinds of prostate disease.
Behavioral problems aren't as common in females, but can happen. The biggest reason in females is risk of disease. Mammary gland cancer is equivalent to breast cancer, and is just as bad. If a female dog or cat is spayed before their first heat cycle, they have less than a 0.1% chance of developing this cancer. If spayed between the first and second heat cycles, the chance jumps to 10%. After the second heat, the risk is about 25%. Ovarian cancer is also a possibility, though not as common as mammary. Within the last few months I have had to remove three mammary tumors from unspayed dogs, one of them highly malignant. And if you have never had a female in heat, it can be very messy.
So hopefully you can see that there are very valid reasons for surgically altering your pets. If done properly, any health risks are very low, and these are very routine surgeries. If you haven't done this, talk to your vet right away. There are no good reasons NOT to spay or neuter.