All kids want their own pet. In fact, they probably want several of them. But, before you give in to your child's wishes, you need to evaluate your child's level of responsibility and maturity and decide which pet is right for them. A bad decision can leave you with a pet that is neglected and not cared for.
For small children, a good first pet to test their responsibility level is a hermit crab. These little creatures require very little in the way of care and are a fun pet to have around. They can be fascinating and your child is able to interact with them to a certain extent. Once your child proves they can care for this simple creature, you can move to something that requires more care.
The next step up are hamsters and guinea pigs. Though they need more care than a hermit crab, they can still pretty much take care of themselves as long as they have food and water. Once your child proves that they are capable of providing food and fresh water on a daily basis as well as keeping the cage clean, you can consider a pet that requires even more responsibility.
Dogs are the pinnacle of the common house pet hierachy. Dogs are extremely social animals so besides requiring food and water, they also require frequent human interaction. Children must accept that the responsibility of caring for these animals requires more than simply feeding them. They need to ensure that they get plenty of attention and exercise. If you do not have a yard, the pet will require a walk at least a couple of times daily. Grooming is also important and the child should bathe the dog weekly. These are things that you must discuss with your child BEFORE you get the dog.
When considering a dog, make sure that the type of dog you get suits your child's personality and energy level also. There's no need to make things harder on both of them by not finding a good match.
If you have doubts that your child can handle the responsibility of caring for a dog, do everyone a favor and wait a little longer. Neglected dogs are way too common and a little planning and testing can avoid many of these situations. If your child is adamant about getting a dog, make them prove their responsibility level in other ways before giving in. Pets can be a great way to teach kids responsibility, but they should at least have the basics down before the dog ever arrives.