I believe God answers our prayers. The thing is, we don't recognize it as being answered positively because it may not go our way. It may be that God's plan for us doesn't exactly include what we are praying for.
A good explanation of God's answering prayers is - yes, He answers all prayers. The answer, however, may be "yes" or "no" or "wait" - you see, what we want may not be part of God's plan. Our God may have a bigger picture in mind with a different purpose than that which you are praying for and about. Perhaps you will get a "yes" - in the future, after other circumstances take place.
I remember hearing a remark someone made, after which she had been praying for something and at some point, met up with another person who had been praying for something different. The two actually, unexpectedly, met each other's needs. The second person asked how this could work out as such - the initial person said "I think we are victims of our prayers" - because, in actuality, both found what they had been praying for, but it came about in a totally different manner than expected.
Maybe you prayed to get to work on time because you were running late. Then in your hurry driving, you encountered many red lights. After you get further, you see an accident that just happened, and realize it was almost you had you not been delayed. So to keep you alive or from injury, you just ended up being late.
When you wonder if God hears your prayers, realize He does, but you may be asking for something that doesn't really go along with God's big picture, and perhaps the prayer will be realized later, or in a different way, or perhaps you are asking for something that has no fit, and would not be granted.
When praying, remember to ask for forgiveness for your sins, and to help guide you to repent. Ask for that which is important, not trivial or material. Ask for blessings for your family and friends. Ask all this in Jesus' name, and make sure to mention "if this is Your will" - so you realize who is in control and acknowledge that. You recognize that God will decide to answer your way, if it is His will.
Be patient - not all prayers are answered immediately. Often there are other building blocks which must take place to get your particular request to the point where it can work. Sometimes your request just isn't in the big picture and you have to let go of your quest. Recognize that God knows best and go with it. Most life situations have a lesson for us - we just have to look for it and see it.