This article is from the Your New Dog FAQ, by Cindy Tittle Moore with numerous contributions by others.
Many people wonder if getting an older dog (of either sex) neutered
poses a problem for the dog. The answer is that it doesn't. Your male
dog will adjust easily to being neutered -- in fact he may well behave
as if he had never been neutered. The most likely change in behavior
is reduced aggression toward other male dogs. Your bitch will not have
any problems with being neutered either. Unfortunately, she may not
derive the health benefits of early neutering if she has already had
more than two estrus periods or is over two years of age before being
spayed. This means that you should be sure your vet checks her for
mammary cancers at each checkup even though she is spayed.
As a general rule, _all_ rescued dogs should be neutered. There are
some special circumstances, such as rescuing a dog of a known breeding
and returning it to its breeder, but these are extremely rare
ocassions and not likely to happen to the average dog-adopter.
Neutering an older dog of either sex will not hurt it at all.