Since this forum is about debate, and debate seems to be about proving a point. Shouldn't debate be a method by which someone changes someone else's mind on a matter?
No. You can have a debate on abortion without expecting either party to change their mind. You (or the audience) can learn something in the process, or just plain practice your debating skills.
This learning process is the supposed reason behind presidential debates. Although I would still enjoy seeing one of the candidates say "You know what...I'd never thought of it that way." Or Kerry: "You've got a point there, George. Who needs an exit strategy, anyway?"
It doesn't seem like it, because in a debate, the opposition to an idea/belief usually just becomes more entrenched in their ideas/beliefs.
So how DO you actually change someone's view on a matter, or is it even possible?
I've heard of using kindness as a way to changing someone's mind, but that seems like a long shot.
I doubt you'll change somebody's point of view, because either A) they'll be so unused to the debate that they'll be defensive enough that they won't believe anything you say, or B) they'll be so used to the debate that they'll be so well-read on the subject that there won't be anything new you can say that will seriously affect their argument.
As far as kindness, well, yeah.

Granted, you aren't going to change somebody's stance on abortion by saying "Pretty please with whipped cream on top", but the complete opposite will just make them feel so insulted that they'll barely acknowledge anything you say, besides to refute it. Your chances go from about .02% to .03% if you're nice*.
That being said, for every one person you argue and fight with, there may be tens or hundreds or thousands (depending on the venue) or more who end up reading your argument. Those people, who have no personal risk in changing their views because they're just silently listening, are the people who you're most likely to influence by being nice. Especially if you're debating something such as ethics or religion, where apparent friendliness will be associated with the success of that worldview. Nobody will want to take on a perspective that will make them dislikeable. Well, most people anyway.
* In the true spirit of debate, these figures are BS that sound about right for my side of the argument.