Okay, you want a pet rat. You are a child--or rather, you are someone who is young and still living under your parents' roof and rules. In this situation, you need to take in two considerations. Can you and WILL you be a good owner, taking care of your pets even when you'd rather be doing something else, even if you "get bored" of them? And will your parents allow you to have rats? (It is their house, and there rules, after all.)
I have always believed rats can be perfect pets for children of any age, but they are living, feeling animals. As a child, you need to remember that your own pet is your responsibility for its whole life. Rats can live up to four years. For those years, you will have to care for their basic needs, including a clean cage, food and water, daily holding, and seeing that they have medical care if needed and have someone to care for them if you go on vacation. Because you are still living with your parents, taking good care of your pets is even more important. Your parents will want you to keep up with the cage cleaning or their house will smell "like rat," and some parents are less tolerant of odor than other. Rats should never smell, and with good litter and weekly cage cleaning, yours won't either. But you must remember to clean the cage every single week.
Parents' biggest concern about their kids having pets is that they (the kids) will get bored of the pets, and the parents will have to take over their care. These are your pets. You need to take good care of them for as long as they live. If you are going off to college in a year or two, don't get rats. You won't be able to take them with you if you live in a dorm, and it is not fair to your parents to have a bunch of pets dumped on them when you move out.
Some parents will expect you to take financial responsibility for your pets too. That means, you have to buy their supplies, their food and litter, and pay any vet bills if they get hurt or sick. A pair of rats is actually very inexpensive--usually. Monthly costs for food and litter can be paid with an allowance or other small part-time job, and you should still have extra money. However, if your rat gets a tumor, or catches pneumonia, or gets seriously injured, you might be looking at a vet bill of $100 or so. Some parents will give you that money in an emergency, but some won't. You might have to make financial sacrifices for your pet by saving up rather than going to movies, buying CDs, or doing other fun things with your extra cash. Discuss emergency vet costs with your parents. If they say they will not pay for your pets, then save your money, and show them you are ready and willing for that responsibility.
Convincing Your Parents
I hear this all the time: "My parents won't let me have a rat. How can I convince them?" First, you need to know why they won't let you have rats. Find that out and then discuss it with them.
Is it a question of responsibility? Have you had pets before and not taken care of them? Will these be your first pets, and your parents don't think you are ready? Are you ready? If your parents doubt your responsibility, think about if you have given them reasons to think that. Talk to them about it. Then, think about how you can show them you are responsible and do it! Don't just keep promising you'll take care of the rats, show them you are responsible. Clean your room and do household chores regularly without being asked. Take over the care for other household pets such as the cat or dog. Don't avoid the unpleasant tasks, do them! Clean litterboxes, walk the dog, take care of food and water... Do everything you can to help out. Don't mention the rats for a while. After a couple months of "being responsible," bring it up again. If they come up with another excuse, then maybe they are not worried about responsibility, but something else is bothering them.
Do your parents just not like rats/rodents? Have they offered to get you a different pet? If this is the case, then your parents have fallen into the unfortunate bias and misunderstanding about pet rats. The first step is informing them. Rats are much less smelly than mice, guinea pigs, and hamsters. Unlike mice, they will not escape and get lost (rats come when called and want to be with you). Unlike hamsters and gerbils, they will never nip. They do not ignore their owners and instead crave attention and affection. Throughout history, pet rats have been compared to dogs. They don't need much space or a lot of time like larger animals (cats, dogs, ferrets, rabbits, etc.) do. Rats are very much domesticated and nothing like wild rats (which can be aggressive, nervous, and everything a pet rat isn't). Find some good rat websites, and show them you know your stuff. Pictures of pet rats being themselves (asleep and cuddly, interecting gently with owners and cats or dogs, just looking cute) could help. The best way to show your parents what pet rats are like is by visiting someone who owns and takes good care of their rats or by babysitting someone's rats while they are on vacation. (Don't use rats in a school class or a pet store as an example. Most of them have been neglected, never or rarely held. They will not act like a well-cared for pet, though they usually are amazingly good natured in spite of such neglect...) Also, remember to tell your parents, that they will never have to see your rats at all, that you will take sole responsibility for their care.
If it's not a question of responsibility or rat bias/fear, maybe your family already has enough pets. Maybe your parents are just dead-set against it no matter what. Just talk to them logically without getting angry or upset. Don't pester them all the time. If they say "no," ask why. If they won't tell you, leave it alone for a while. Get a good rat book. Wait a few months before bringing it up again. Sometimes, parents can't be convinced. I think that's why there are an awful lot of twenty-something year olds with their first pet rats...
As a final consideration, if your parents say you can have rats but under some circumstances that would be a risk to your rats' well-being (such as, they have to live in the garage or you can get only one), don't take them up on it. Under such circumstances, your rat will suffer and you will have a bad experience with a sick or neurotic animal. Your parents will likely think either rats are bad pets (and all pets are "bad" if they receive the wrong kind of care or housing) or you are not taking care of them well (even though you might be doing the best you can). Tell your parents why rats cannot be kept under those circumstances. If they refuse, then that's the end of it for a while. Either talk to your parents about it later or look into another pet that can live happily under your parents' rules.
Good luck, and remember that your rats will love you and they will need you! Take good care of them, and your rats will be happy, you will be happy, and your parents will be happy.