Rejoice with those who rejoice, and weep with those who weep. (Romans 12:15)
One of the reasons God lets us suffer in life is so we can understand the suffering of others and be able to comfort them--to do unto them what we would want others to do unto us. Paul lays out the progression of comfort in suffering by saying that God comforts us when we are hurting so we can comfort others with the same comfort by which we were comforted (2 Corinthians 1:3-4). When we suffer, we should receive the comfort of God and remember it so we can replicate that comfort for another. We don't have to pray for suffering--it will find us easily enough. But we should pray for a spiritually-empathetic heart to feel the anguish of others and be prepared to comfort them as we ourselves would want to be comforted.
(Copied from today's Turning Point with David Jeremiah)