On Sunday at my church this whole question of "why does God allow suffereing" was discussed. The way it was explained and the way
I believe is that God gave us free will so that we could choose to love Him. If He made us to love him then the love would be no more real than if we went into a toy section and picked up a doll with a pull sting that said "I love you". The love would be ingenuine and wouldn't mean anything, it would be lipservice. With that free will we are able to do good or bad and suffering comes from the bad choices and sin that we make/do or that others have made/done. These choices are like a water droplet in a pond. It may seem insignificant at first, but the effects ripple out indefinatly. God loves us, and cares for us, but for there to be a relationship we have to return that love. For those of us who believe in Christ and His death being the way to our redemption then when we die and go to Heaven then we will no longer suffer, there will be no pain, no fear, no death, etc... that is our promise from God. On earth we are not safe from pain or suffering, God never promised that. The suffering that we endure on earth teaches us compassion and empathy and helps us to remember to turn to God in bad times.
To a small child going to the doctor for a vaccination is a terrifing thing, but their parent takes them anyways. The parent lets the child suffer because the vaccination will protect them from future harm. The child doesn't know that at the time, all they know is that it hurts and that they are scared. We are like that child, we don't understand the reasoning for the pain that we are going through, but our parent, God, does understand and does know why we suffer. Like all things spiritual, it requires faith.
"All the while making faces like a baby platypus who forget to take some Beano before eating a chimichanga." FindingNamo in reference to Jessica Simpson's singing.