My boyfriend recently asked that we take a break. I really want him back. If I leave him alone for a little while and give him the space he requested, will he start to miss me? What are the chances of him coming back?

He may start to miss you, and he may start to date someone else, you never know. But if he wants a break you have no choice, since if you don't, it can only make it worst at times

Yep
It's best to give him what he wants and that's a break. If you pursue him at this stage he will just pull away harder.

Yes, give the break, back off, and never contact him again, until he contacts you. And if he wants to get back together and you still want him back. Make sure you understand fully why he wanted the break in the first place and make sure it's not going to happen again. Take care and best of luck.

Give him what he asked for, and leave him alone to enjoy it. Nobody knows if he will ever come back, but hassling him will drive him further away.