Should you get a "pet" for your pet? This question is often asked of veterinarians, but the answer is not as simple as the question. Many people want to get another pet so the resident dog or cat will have a playmate during working hours. The intentions are noble but sometimes they are done out of guilt and not in the best interest of the pet. In many ways, pets are like people; just putting two together does not mean they'll get along.
In a perfect world, they would. Of course, in a perfect world, there would be peace on earth, perpetually low gas prices and little or no back pain. The worst-case scenario is a nightmare indeed: the animals injure each other and wreck the house. Instead of one pet that you believed was lonely, you have two who are unquestionably miserable.
Cats are especially territorial and not prone to welcoming newcomers. This isn't to say that all cats will hate a fresh companion. Cats that have been socialized with other kittens when young will more likely accept another cat or even a small puppy.
Incidentally, don't get a "playmate" for your cat in the form of an animal that she considers prey. Getting a bird or hamster for your cat will very likely result in tragedy.
The same goes for dogs. You should be selective in what sort of playmate your dog may enjoy – if he needs one at all. A dog tends to be more accepting, but remember – they are very hierarchal. A dominant dog may try to usurp the resident dog's position. If both are dominant, they may fight it out.
The best solution is to avoid the problem in the first place by getting two pets at the same time, while both are kittens or puppies. They'll grow up with each other and consider all of you to be one big family.
You could also hire a sitter to walk your dog or visit your cat during the day, which may break up the tedium. A solution that is gaining popularity is to drop dogs off at doggie day care, where he gets to play with human handlers and other dogs. (Your dog will have to be carefully screened before being accepted to avoid aggression.)
Although some facilities do offer kitty day care services, cats are more stressed when they are taken from the home and placed in a strange facility day after day. A visitor they like is much more comforting for a cat.
If you think your pet iguana is lonely, you need to brush up on your knowledge. Except for breeding, reptiles should not, as a general rule, be housed together. The same goes for many other pets. Research before you arbitrarily decide if your pet is in need of company.
That said, some animals are quite social and do better with a friend. Rats are very social. They enjoy the company of people and other rats. Birds such as finches, canaries and lovebirds also thrive with a companion. They are so devoted that many bond with their mates for life.