Time and time again we see Jesus doing miraculous things followed by a pharisee asking him for a sign to prove he is the Messiah. Check out Luke 11:14-16.
It seems we are never looking for the sign we are actually given. I prayed for rest to come to my wife and child one night and before I knew it I was rocking the little guy to sleep at 2am while my wife got some much needed slumber. This was an answer to my prayer, but not what I had anticipated.
I was once told to never pray to God for patience unless I had time to sit in traffic. He doesn't just grant these things, it would appear that He gives us opportunity to grow in the area we pray about. Embracing this hard fact is paramount to seeing how God has answered some of your prayers.
We tend to want our prayers answered, but at no personal cost to ourselves. But personal sacrifice is where it is at! This whole rigamarole started when God chose to share His universe with us. He sent His only Son into the world not only to teach this principle, but to offer himself up as the ultimate sacrifice to atone for our sins.