Mine would be to see what the world would be like if Archduke Franz Ferdinand hadn't been assassinated. That would have changed just about everything that happens in the next century. No WW1, possibly no Great Depression (not sure about this one), no WW2, no Pearl Harbour, no Holocaust, no Nukes dropped in Japan, no United Nations, no Israel, no Cold War, no Space Race, no Vietnam war, no Nuclear arms build up, no American training or equipment with the Taliban, no 9/11 attacks, and no war on terror.
Though some of these may have very well just happened later in time, but with a very different setting and date (or maybe even with entirely different people involved)
Also i just want to mention, this idea came from my Social Studies (its like history class) teacher in High school, but she told me this 2 years ago so sorry if i get any details wrong