This worked for me:
Tell your friends you want a webcam for your birthday. They will get it for you. Your parents aren't going to make them take it back.
The worst they will do is not let you use it fo the time being, but tell them that you will only use it when they are home, or during certain hours of the day (so no midnight chatting with strangers), and let them look over your shoulder during a conversation with one of your friends when he/she is using their own webcam so your parents can see how it works and who else has a webcam.
Remind them that part of having webcam chat means they can see exactly who you are talking to...its almost a bonus for them!
To people above me, webcams are not just sexual. I used mine all through high school and into college to talk to my friend in Alaska since I live in the lower 48. I've never done anything sexual over webcam...in fact, sometime having a webcam on is more annoying than it is practical since everyone can see everything you do. People, especially predators, are more likely to have regular chat WITHOUT a webcam since it allows them to keep their identity or flaws hidden.
Having a webcam can actually be a safety precaution because it allows parents to actively see who their kids are talking to.
I would recommend you establish ground rules with your parents: no using webcam unless the other person is using webcam (so they can see who it is...or else no using webcam unless your parents physically know the other person...like one of your friends), no using webcam with (or even talking to) strangers, no using webcam when they aren't home, no using webcam past 10 pm (or so). My parents used to unplug mine at 10 and put it in the kitchen.
Besides...if parents are so worried about online predators why do they give their children instant messaging to begin with?