How do I know God answers prayers, even if nothing happens? I've asked God to give me a sign that He is hearing me, but He hasn't. Sometimes I even wonder if it's worth it to keep on praying. — Mrs. C.B.F.
Prayer is one of our greatest privileges as God's children, and even if God doesn't seem to answer your prayers at first, don't stop praying. God loves you, and no prayer goes unanswered.
Jesus once told a story about a poor widow who repeatedly asked a corrupt judge to do what was right. (You can read it in Luke 18:1-8.) Repeatedly the judge refused—not because her request was wrong, but because he just didn't care. But because of her persistence, he eventually gave in and granted her what she deserved. In a far greater way, Jesus said, God (who is righteous and does care for us) hears the prayers of His people, and we must never give up.
But let me add two things. First, realize that sometimes God is actually answering our prayers when we don't realize it—and the reason is because His answer may be "No" or "Wait." Yes, we think we know what's best for us—but God sees the whole picture, and sometimes He lovingly refuses to give us what we request, because He knows it isn't according to His perfect plan.
Second, remember that we have the privilege of coming to God only because Jesus Christ died for our sins. Have you given your life to Him? If not, let your first prayer be one of confession and faith, asking Him to come into your life as your Lord and Savior.