There are certain kinds of prayers God DOES want to answer. We can determine what kinds of prayers those would be from the Bible. These include;
in Jesus' name prayers
not my will, Your Will, prayers
intercessory prayers for others
groaning prayers - where we let the Holy Spirit pray for us
Let's review each one briefly, so we have fresh in our minds the prayers God does want to answer.
From Psalm 51:16-18, "My sacrifice, O God, is a broken spirit; a broken and contrite heart you, God, will not despise." we know that God is always tenderly inclined to anyone who comes to Him with a humble, repentant, or broken and contrite heart. That means we come confessing our sins and need of Him, and we are asking for forgiveness. So we need never be afraid to approach God, when we are ready to confess sin.
In John chapters 14 and 15, Jesus Himself is quoted at length, talking about abiding in Him, and praying in His name. The condition is that we abide in Him, and let the words of Jesus abide in us - that is, we obey them - then we may ask the Father in prayer, for anything that Jesus might pray for, using His name, and He promised that the Father would grant it. "If you remain in me and my words remain in you, ask whatever you wish, and it will be given you. This is to my Father's glory, that you bear much fruit, showing yourselves to be my disciples." (John 15:7-8)
Jesus guaranteed that these are prayers God DOES want to answer.
Confession of sin is another type of prayer God does want to answer. "If we confess our sins, he is faithful and just and will forgive us our sins and purify us from all unrighteousness." (I John 1:9) We will never be ignored if we come humbly in prayer to confess our sins. God does want to answer confessional prayers.
This is a conditional prayer too. We ask for what we really want or desire, but we give God permission to overrule and cancel our request if it is not according to His far better will. We see Jesus praying this prayer in the Garden of Gethsemane just before He was arrested and taken to a mock trial and then His crucifixion. "Abba, Father," he said, "Everything is possible for you. Take this cup from me. Yet not what I will, but what you will." (Mark 14:36). God may not grant us what we desire, but such prayers God DOES want to answer! Later on, we will be glad for the way He answers.
Many dear prayer warriors have testified that when they were going through a deep struggle to give up their natural will and desire for God's will - that was when the Spirit of God was nearest to them.
We don't usually pray for others often enough, nor hard enough, but God loves to hear us pray for His servants, our families and friends, and even the many people who have not heard the gospel and had a chance to repent and receive Him as their Saviour and Lord. Let's feel free to turn away from praying just for ourselves, and pray for others too.
Just two examples of men who interceded for others are; Abraham, in Genesis 18:20-33, and Jesus in John 17:20-26.
I read once that no one is saved unless someone has prayed. I have watched closely when I hear testimonies and this has proven true in almost 100% of them. As for the rest, there may have been someone praying that the one testifying was not aware of. All this has motivated me, so that I pray for earnestly for the salvation of many who never hear of me doing so. Therefore, I believe we shall have some surprises in Heaven, for I am convinced these are prayers that God DOES want to answer too!
Romans 8:26-27 speaks of times when our spirit groans in spiritual agony - we are unable to form words for praying, but God's Holy Spirit knows us completely, and He will interpret those groanings to the Father in prayers. We do not have to be articulate at all times. When we are overwhelmed just come to the Father in an attitude of prayer, cry out from the depths of your spirit's feelings, and the Holy Spirit will convey what You are feeling and needing as He prays for you.
What do you think? If the Holy Spirit is praying for us, aren't those prayers God DOES want to answer?