I'm listening to a podcast sermon-type thing about "unanswered prayer" (from crosswalk), and it's driving me crazy. I don't have a problem with prayer being much more powerful when it's aligned with God's will and His plan; what I take issue with is the concept of "unanswered" prayer. God never leaves any prayer unanswered. I think what causes us to stumble over this is that we don't know what an answer is. God answers prayers in one of three ways: yes, no, or later. The reason some people think their prayers remain unanswered is that they don't hear the answer they want. They don't recognize a "no" as an answer to the prayer. And "later" is probably even worse--who wants to wait for God to answer a prayer? We want results NOW.
Sadly for us humans, God doesn't work that way. He's on an eternal schedule, not constrained by our deadlines and impatience. If I pray for a friend to be healed, but that friend remains sick, it's not that God ignored my prayer; it's that He said "no." If I pray for God to move a mountain for me, and it stays where it is, that doesn't mean that God hasn't answered, it means that he's either answered "no" or "later" (The secret for figuring out which? If there's no definitive answer, it's probably a "later".)
How do I know this? Aside from all the places in the Bible that talk about "waiting on God" (also here, here, here, here, and here, among others) and persevering in prayer, I've seen it in my own life. Any number of times, I've prayed for something for months (and occasionally years) without hearing back from God. Then--seemingly out of the blue--I'd get an answer that was beyond my wildest hopes.
So don't believe the nonsense about "unanswered" prayer! Maybe you just haven't gotten the answer you wanted. Just remember (this one's hard for me) God knows what He's doing, and he's smarter than us. Trust Him. Oh--and it's always worth the wait.