Yes.
One recent example is my son (9mo. old now). My wife had experienced some abdominal pains around the 32nd week of the pregnancy and the doctors put her on bed rest. During other hospital visits, we were told that she would more than likely deliver by the 34th week if she took it easy, but probablly wouldn't make it much past that time. I prayed for her and our baby - that our son (didn't know at the time he was a he) would be born at full term. I remember a peace came to me about the situation and knew it was from God. I told people that he was going to be born full term because I knew before the time came, that God had answered that prayer. When we went in for the doctor's appointments to check on the progress of the pregnancy, the doctor's were baffled and kept commenting, "you should be having this child right now. We don't know why you aren't."
He was born on the 40th week. Due to a discrepancy in testing, the doctors are not sure if he was a week early or a week late. I say he was born at 40 weeks to the very day, exactly as God planned. One prayer request was that God would get the glory for answering that prayer and again, He gets the glory here.
God answers prayer.