Do I believe we will ever see world peace? Not in my life time! I think the first time there will be world peace is during the Tribulation. (And since I believe in a Pre-Tribulation Rapture, I will not be on earth during this time). The first few years (3.5 ish) will be peaceful because of the peace treaty. Then there will be wars and worse things until Christ returns for the Battle of Armageddon. Then there will be peace for 1000 years (the Millennium). This will be followed by one final war.
So, should we pray for peace? Yes. I think that God does listen to our prayers. I think that if there is enough pray then the wars won't be so terrible - fewer deaths, fewer injuries, shorter. But there will still be wars. Why? Because we humans are greedy! We want land. We want power. As a result, men will fight to win the spoils of war. As we approach the last days, the wars will increase because of the rising evil in the world.
There is a lot more I could say about the Tribulation, wars, etc. But I know that even true Christians differ on these issues. I want everyone to remember the most important thing - belief! Things like the Rapture and creation are important to how you interpret the Bible, but saved men stand on all sides of the fence on these issues. Debate is fine, but arguing over these issues is not. This is especially the case with non-believers. The most important thing is to show them who Christ was and lead them to salvation. It is not if they believe in creation or evolution... or how they feel about gay marriage... or about abortion...