The first of three answers to prayer God can give is "YES!" Solomon, as a young and inexperienced King of Israel, asked the Eternal for wisdom. This trait, which he lacked, was essential in order for him to effectively and righteously rule over the Israelites. Not only did he receive enough supernatural wisdom to make him the WISEST human in history (before or since), he received unmatched riches and honor (1Kings 3, see also 2Chronicles 1:10 - 12)! This is one of the most awesome answers a human has ever received from a prayer.
The early New Testament church, after Peter was arrested by Herod, offered up fervent prayers on his behalf. The answer they received from God was nothing short of miraculous. He personally sent one of his angels to free Peter of his chains and escort him out of the prison in which he was held (Acts 12)!
The Bible contains many other examples of people receiving a positive, and fairly quick, response to their prayer. They include Samson (Judges 16:26 - 30), Gideon (Judges 6:36 - 40), King Hezekiah (2Kings 20:1 - 6), Elijah (1Kings 18:36 - 38), Daniel (Daniel 9:3 - 23), Paul (Acts 9:9 - 12) and numerous others. God even promises positive answers to people's needs, during the Millennium, BEFORE they have a chance to ask him (Isaiah 65:24)!
One of the three answers to prayer we usually do not want to hear is No! During his second missionary journey, Paul wanted to travel to both the western and northern part of Asia Minor but was forbidden to do so (Acts 16:6 - 7). Paul also prayed for a painful affliction to leave him and was denied (2Corinthians 12:7 - 9).
God will usually deny requests that seek to indulge selfish and sinful desires (James 4:1 - 3). He will also not respond to those who are willingly pursuing a sinful and unrepentant life (Proverbs 1:24 - 28, Daniel 9:13 - 14, 1Peter 3:12, etc.). There are also times when he may seem to deny us but what he wants is for us to be persistent and faithful in our prayer (Luke 11:5 - 10, 18:1 - 7). Even if our requests are innocent and righteous, he may not grant them because they do not fit his overall plans and timetable.
True Christians should be willing to admit that they lack the wisdom and perspective to know what is ultimately good for them or others. If we feel the Eternal is slamming the door on our requests, we need to go to him in prayer and ask him to reveal his will for us. We need to adopt the same attitude as Jesus, who made requests to the Father like we do, but always deferred to his perfect will (Matthew 26:39, 42).
Perhaps the most difficult of the three answers to deal with is "wait," which is another way of saying "yes, but not right now." Jeremiah the prophet had to wait ten days before God revealed which way he and a large group of people should travel (Jeremiah 42:1 - 7). The Eternal has promised those who cry out to him that he will avenge how they have been treated but at a later time (Luke 18:1 - 8). Having to wait and exercise patience is not easy, especially in a world that craves instant gratification. Yet the character to wait patiently and endure is something our Father wants in us (Romans 5:1 - 5). Believers can be confident, in faith, that they will receive answers to their prayer (Psalm 10:17, 65:2, 1John 5:15).