I try to keep an "attitude of prayer" going at all times, but I don't do formal prayer nearly enough. Hard to explain that. But in answer to your question, I have absolutely had direct, specific answer to prayers in my life. Interestingly, like Dani, one of the first that I can point to was a firm "NO" in answer to my prayer for healing for my mother. She died and I got mad about that. Had all the faith in the world that she'd be healed, prayed faithfully for that healing, along with countless others, but it didn't come. She didn't get up and walk out of the hospital. It took me a lot of years to get over that. All on me, of course, as God is and always will be utterly faithful and right. But I needed to learn that sometimes, He just isn't going to give us what we want, no matter how much we want it. I was young then, too, a fairly new Christian, so that played a part. Since then, though, I've learned to trust Him in all things and I've felt His direct touch in my life in answer to prayers. One that stands out strong for me was at my sister's funeral. We were very close. I loved her a great deal and while I"d prayed for her healing from cancer, I'd also accepted that healing might not be God's will for her life. So, when the call came that she'd died, I accepted it. I grieved, but I accepted it. Then, at the funeral, it just hit me like a kick to the chest. I was thinking about our mother, about my sister, about how very much I was going to miss her, how much I already missed our mother. And the weight of the grief was smashing down on me like a tidal wave. Losing my mother broke me in a lot of ways. Took me literally years to even start getting back to something even approaching "normal." By the time my sister died, I knew full well that I had clinical depression and that what it felt like when it was surging to life. I sat there, feeling it boiling up inside me, choking me, and I just closed my eyes and told God I couldn't do it. I was at my limit. I was literally a breath away from screaming out loud and collapsing in a heap. I told Him I needed Him to help me, to get me through it. And in that instant I was flooded with a peace and comfort unlike anything I'd ever known. The weight on my body just evaporated and the impending collapse vanished with it. I didn't stop grieving for my sister or my mother. I still grieve for them both today. Miss them like crazy. But God took the horrible darkness and just swept it aside. He gave me the strength I so desperately needed the moment I needed it.
There have been other times He's worked in my life. Many other times. The real point is that the answer to your question is that God ALWAYS answers our prayers. Sometimes we just aren't willing to accept what He's said. Sometimes, we don't want to take "no" for an answer.
I am so incredibly thankful that God is there, that He hears us and responds, even when we're too thick-headed to listen to His response. And I'm so glad that He loves us enough to abide our tantrums and pouts when we don't get our way. God is just so incredibly good!