If all I had to read were the daily headlines, then yes it would be very easy to become discouraged and wonder if there was any hope.
But I also read something else every day and that is the Bible. And because of that, I know there is hope for the future. Yes, we live in a world that is filled with evil and violence, and the Bible is realistic about that. Jesus even warned that evil will grow worse before He comes again, and "Men will faint from terror, apprehensive of what is coming on the world" (Luke 21:26).
Why is there hope? Why should we pray? First, because God is still on the throne. In spite of all the evil in the world, the forces of Satan cannot overcome God, and some day His kingdom will come. Although we may be unaware of it, God is at work behind the scenes, and He often works in response to our prayers. How much worse off would our world be if people weren't praying?
Second, we should pray because God is still at work in the hearts of men and women, calling them to Christ and changing them by His Spirit. Pray for God to guide the leaders of the world (even those who seem opposed to Him). And pray also that God will bring spiritual revival to His people beginning in your own heart and life.