As a Christ-follower (fun fact: my husband says I use that term all the time as opposed to Christian. It's true, I think "Christian" is overused and more times than not, incorrectly used), I fully believe in the power of prayer. Are my prayers always answered right away with a definitive answer? No, but I still believe in the power of it.
When we pray, we tend to spout off a to-do list to God: "God please fix this. God please do that. God please make this mean person disappear!" It's okay, I'm guilty of it too and I will be the first to admit it.
What if we stopped giving God a to-do list, but rather prayed for HIS will to be done, HIS to-do list to be done? That's a pretty radical thought right? So let's turn those previously mentioned to-do's above to be God-centered:
"God please fix this."
"If it's your will God, please fix this. If it's not your will, I will still praise you always."
"God please do that."
"Thank you God for allowing these events to occur in my life. I pray that you will continue to lead me where you want me to go. Whatever happens God, I will embrace the circumstances because of the hope I have in you."
"God please make this mean person disappear!"
"God, thank you for this person's life. Thank you for bringing them into my life. God please help me to be a light to this person, and my words are reflective of you. And God, please control my anger towards this person."
Do you see the difference? When we stop making demands for our sake, but start embracing demands for His sake, I fully believe the power of prayer is real. It's hard to not be self-centered and want what we want; trust me, I would know first-hand. But oh the wonders of what He will use you for when you stop saying me, myself, and I, but instead, You, only You, always You.
So I challenge you with this - move yourself out of the way and stop making demands. Rather open your prayer life to the One that can actually do it all. And do it joyfully!