The title of this article may startle the readers! Yes, there are prayers that God may not answer. It is hard to believe this in a world where there is so much of talk about miracles, deliverance and so on. We are made to believe that God answers prayers unconditionally. We are also made to believe that certain places and certain people have so much charisma that anything they pray for will be answered. So we tend to flock to these places and around this people to get our prayers answered. We are encouraged to subscribe to some prayer plans (quite similar to some saving plans) that for a small subscription our children will be prayed for from birth to their adulthood. Childhood ailments, successful education (a main worry for Indian parents), job security and marriage are all covered in these plans. All that we need to do is to subscribe, sit back and relax for the rest of your life!
However, God doesn't answer prayers unconditionally. He is not a slot machine, where the machine delivers what one want by simply inserting a coin or token without any questions.
God does not answer prayers when there is sin in our lives. God want us to receive his forgiveness and correct our lives before coming to him. God has moral demands and he insists that our lives be according to his will before he grants us our requests. King Saul prayed to God for help against the Amalekites, but he was terribly defeated. God did not answer his prayer because of sin in his life (1 Samuel 14:37, 1 Samuel 28:6, 7). David prayed for the healing of the child that was born in his illegitimate and sinful relationship. God did not answer, the child died. Though David had repented, it was God's will that he feel some pain of his sinful action (2 Samuel 12:13-23). However, God allowed the second child (Solomon) in the same wife to ascend to David's throne later.
God also doesn't answer prayers that are not in line with his will. His will is supreme above all our wills and his will is perfect and flawless. He knows what is best for us. So he answers prayers only according to his will. Elijah was a great man of prayer. Bible says that he could stop rain (James 5:17), he had brought down fire from heaven that burnt the sacrifice, dried up the water and even melted stones of the altar (1 Kings 18:32-38). However, God did not answer one of his prayers: He wanted to die but God did not allow him (1 Kings 19:4; 2 Kings 2:11). Because that was not in God's will that he die at the time he wanted. So was also Jonah who wanted to die but God did not allow him to die when he wanted to die (Jonah 4:3). Saint Paul was not a sinner and but though he prayed for healing of his physical ailment (we don't know what exactly it was) God simply refused instead gave him the grace to live with it (2 Cor 12:7-9).
Thirdly, there are things in our control that God will leave us to address than bringing it to him, especially matters that have to do with our character and our moral life. For example, God is not going to answer the prayers of those who pray that they will be more humble because being humble is in their control. If they want to be humble all that they need to do is to go ahead and be humble! If people pray that God make them more liberal, I don't think God is going to make them liberal in their giving because they just need to go ahead and start giving. Many times such prayers are used to shun human responsibility and put the blame on God! However, we need God's grace to live lives pleasing God. So, God is certainly going to grant the grace to be humble, more liberal in giving etc. Nevertheless, doing it with the grace that God provides is our job.
Now let us turn the question on its tail. Instead of asking what are the type of prayers God will not answer let us see how to pray in a way that God will answer. God answers prayers from hearts that are right with God. Secondly, God answers prayers that are according to his will and thirdly, God want us to do what we can do depending on his grace instead of using prayer as an excuse.