Yes, God hears our prayers. The Bible consistently assures us of this. He is omniscient and knows everything, including our prayers, whether spoken out loud or in our minds. Prayer is personal and heartfelt communication with God where we express our thoughts, needs, gratitude, and desires and where we listen to His response as He reminds us of Scriptures and truths to shape our hearts and minds. God desires for us to call out to Him, and He listens to those who call out to Him earnestly and who seek Him with humility. When we pray, we are called to pray according to His will. God knows our hearts and needs, and He will answer our prayers according to His will in His timing. While God hears every prayer, the Bible warns us that there are some things, such as continuing in sin or ignoring God’s commands, that keep God from listening to our prayers. At the same time, God’s ears are attentive to those who genuinely seek Him, inviting us to come to Him in prayer and to trust in His perfect plan and timing.
Just because it seems that God does not hear our prayers does not mean that He does not. A delay in response also does not necessarily mean God is not listening because of our sinfulness. Many times, God answers our prayers in unexpected ways. For example, you might pray for a specific job, but the job goes to someone else because God has something different in mind for you. Or perhaps you pray for release from a particular hardship, but it is God's will that you go through that hardship because, from it, He brings about healing for past hurts.
If we feel like God is not listening to our prayers, it is wise to examine our own hearts. When we find sin in our lives, we should repent and confess; God is faithful to forgive (1 John 1:9). But we should also continue praying. The Psalms are a good demonstration of just how honest and vulnerable we can be with God in prayer. We can admit to God that we are afraid He isn't listening to us and ask Him to show us the reason or to give us peace in the silence. In Luke 18, Jesus "told them a parable to the effect that they ought always to pray and not lose heart" (Luke 18:1). Persisting in prayer, especially with a malleable heart that is truly seeking God's will and is willing to listen to Him, is appropriate.
Remember that our faith is in God, not in the way we pray or in the specific outcome of our prayers. We can pray for specific things and outcomes, but we ultimately pray for His will to be done. We can imitate Jesus in the garden of Gethsemane (Matthew 26:36–46). The Father heard Jesus's prayer, but He did not allow the cup to pass. Jesus was still crucified on our behalf, and willingly, because of His great love for us. Jesus prayed for God's will to be done, and it was. Salvation was made available to all of humanity (John 3:16–18). Because of that, we, too, can approach God in prayer. We can trust that He hears us. We can also trust that He will respond as He knows best. So, we submit to Him, approach Him boldly and eagerly with confidence, and trust Him with the outcome. What we most want is for His will to be done and for ourselves to be transformed to be more like Him (Romans 8:28–29).