First, God answer some prayers, "Yes!" Numerous examples of God granting requests made in prayer could be cited in scripture. During a battle with the Amorites, Joshua prayed that God would cause the sun to stand still, and not allow the day to come to an end, until the Israelites could finish defeating their enemy (Joshua 10:12). God granted his request (verses 13-14). King Hezekiah prayed that God would spare his life (2 Kings 20:1-3). God granted his request by giving him fifteen more years (verses 4-6).
Second, God answers some prayers, "No!" The apostle Paul prayed three times for God to remove "a thorn in the flesh," evidently some physical problem (2 Corinthians 12:7-8). God did not grant Paul's request (verse 9). In Gethsemane, Jesus prayed at least twice that He would be spared having to go to the cross (Matthew 26:37-44). From our perspective, we can be thankful that God did not grant Jesus' request, that He allowed Jesus to die on the cross to pay the price for the guilt of our sins.
Third, God answers some prayers, "Wait awhile..." Twice Abraham tried to reason with God as to how he thought God should fulfill the promise He had made to Abraham as to giving him an heir (Genesis 15:1-4; 17:15-21). God provided Abraham an heir, fulfilling God's promise to him, but not according to Abraham's time-table and not in the ways Abraham suggested. We have a tendency to want things right now, but God knows the right time.
As noted earlier, there is a fourth way in which God responds to the prayers of a specific group of individuals. God, being God, knows all, sees all, and hears all. But, the scriptures seem pretty clear that God can choose to simply not listen to the prayers of the unrighteous (Psalm 18:40-41; 34:14-16; 1 Peter 3:11-12). How awful, how tragic, to be so caught up in a lifestyle of sin that it could cause God to not listen to your prayers!
Prayer is a wonderful blessing from God. Of course, God knows best what we really need, even before we ask. But He wants us to ask, to demonstrate, by asking, our realization of dependence upon Him and our faith in Him. In order for God to answer prayer we must first go to Him in prayer. James notes that in many cases blessings are not given because we do not ask (James 4:2). Let's utilize prayer regularly and frequently, and let's remember that God can answer prayer in different ways. Just because we may not receive the exact answer we want in the exact time frame in which we want it does not mean God is not listening or answering our request. He may simply be answering in a different way than we desire. But, God knows best...