Prayer means different things, so we have to make sure what exactly we are speaking about. There are petition prayers, there are prayers of thanksgiving, there are communion prayers, etc.
If you're just speaking of petition prayers, the bible does show instances where God changes his mind because of prayer. It's no different than a child asking his parents for something, where they hear the kid out, and then do what he asks.
Yea, I'm pretty much just talking about petition prayers.
But there's a difference between a fallible, limited human parent and a perfect, all knowing, all powerful GOD.
If my child asks me for something, he's providing me with information I didn't previously have. It's perfectly OK for me to say, wow, I didn't know you felt that way. Since I now have new information, my conscience dictates that I take a new course of action. It would be a sign of an evil man if I said, I know my child wants X, Y, or Z, and I might give it to him, but first I want to see him squirm. I want to see him beg.
But God already knows everything that you told him. He knew how badly you were going to want it before he even set the plan into motion. And I just can't think of a reason why God wouldn't just make your wishes a part of his plan since he was going to do it anyway.