"Have mercy upon me, O Jehovah; for I am withered away: O Jehovah, heal me; for my bones are troubled." (ASV)
Healing from God is often a controversial topic, even among Christians. There are those who believe that God will automatically heal anything you pray about, as long as you have enough faith. There are others who believe that God does not heal anymore, that's something He did while He was here on earth, and He won't do it until He comes again. Then there are those of us who are somewhere between those two concepts.
I certainly believe that God still heals bodies as well as hearts and souls. I've seen it happen. I also have seen times where healing did not come, despite the heartfelt prayers offered up. I don't for a moment believe it had anything to do with those in prayer not having faith. I don't think God is obliged to heal someone just because we ask (or in some cases tell!) Him to.
We all know the miraculous stories of God healing His people, but what about the times in the Bible when He didn't? Paul writes "And by reason of the exceeding greatness of the revelations, that I should not be exalted overmuch, there was given to me a thorn in the flesh, a messenger of Satan to buffet me, that I should not be exalted overmuch. Concerning this thing I besought the Lord thrice, that it might depart from me. And he hath said unto me, My grace is sufficient for thee: for my power is made perfect in weakness. Most gladly therefore will I rather glory in my weaknesses, that the power of Christ may rest upon me." (2 Corinthians 12:7-9 ASV) As the man who penned the majority of the New Testament, I think it's safe to say that Paul had faith.
The point that Paul makes here is that sometimes injuries, illnesses, etc. are given to us for a reason. In Paul's case, it was to keep him humble, and I think that is often the case, but I'm sure that God has many other reasons for allowing inflictions such as Paul's thorn. I don't think it's really for us to know why God allows such things, but rather to trust Him to do what's best.
At the same time, I don't for a moment believe that the answer is always no. After Christ ascended to heaven, we know that His followers continued to heal people in His stead. The New Testament lists many times when Peter, Paul or another of these earliest Christians performed miraculous healing. And we know that this gift was given to others as well. Paul wrote "And God hath set some in the church, first apostles, secondly prophets, thirdly teachers, then miracles, then gifts of healings, helps, governments, divers kinds of tongues." (1 Corinthians 12:28 ASV) He was quick to add though that not every Christian will have every gift.
So is it still worth asking God to heal us? Is it still valid to lay hands on loved ones? You bet it is. Pray for the sick, the injured, those who are in need of every kind of healing, but don't curse God if the answer is sometimes no.