Yes, I noticed you said you don't care what type of dog you have. This in itself is quite a naive and irresponsilbe thing to say. All dogs are different and some dogs will not be suitable for your lifestyle and living arrangements so you must research different breeds and all that to decide which one is most likely to fit with your household and lifestyle. I would suggest a smaller or medium sized dog with a coat thats easy to maintain and that isn't too exercise demanding etc.... Something like a Springer Spaniel, Siberian husky or Border Collie would be an absolute no no for somebody in your situation. It takes somebody who knows about dogs and has experience with them to successfully own breeds like that and I'd never recommend breeds such as those as first dogs for anyone.

Also, your parents probably worry that you'll lose interest after so long and leave it to them to look after it. Like the others say, you can only prove to them that you are responsible and are willing to take proper care of the dog for up to 16 years or even longer.....remember that dogs do live a long time and you have to see yourself still taking care of them everyday 10 years down the line. Also, they slow down and become less exciting when they're old and will cost more in vets fees when things start going wrong more. You also have to take into account possible vets fees when the dog is young.

Maybe if you offer to walk a friends, family members or neighbours dog each day, your parents will be able to see that you are dedicated and are not going to allow the novelty to wear off. Also, look into dog behaviour and training and all the ins and outs of dog care other than basic feeding and walking....You really need to educate yourself before even thinking about taking on a dog...just nagging the parents for one isn't the best option.

Obviously, we don't know your parents so I can't guarantee they'll say yes even if you do everything thats been advised but you might just up your chances and you'll learn a hell of a lot whilst you're at it which will do you no harm at all. Even if you have to wait until you're older and have your own place, at least you'll have built up the knowledge about dogs that you need to own one without problems.