The Twilight Zone: "Back There"

In this episode a man named Corrigan inadvertently time travels back to April 14, 1865, which happens to be the day that President Lincoln got shot. So of course he has to go and warn people so he can prevent Lincoln's death. This of course makes everyone just think he is drunk or crazy and they don't believe him, and he is taken to jail. Only one of the officers believes him and he goes and tries to find more security guards for the president. Meanwhile, a man comes to the jail and offers to take care of Corrigan. He tells Corrigan his name is John Wellington, and takes him to his home and poisons him. Corrigan soon passes out and John goes to the theater. Later, Corrigan wakes up but can barely move, he collapses again and the police man who believed him comes in a few seconds later. Corrigan soon figures out that John Wellington is actually John Wilkes Booth. Just then, they hear the news that Lincoln has been shot. A little while later Corrigan gets transported back to the present. He goes back to his friends he had just been talking to and realizes there is a new guy there, and this guy had originally been a servant there, before he traveled back in time. He was rich now though because of what Corrigan did. The fact that the one police officer believed him caused the police officer and all of his descendants to be rich and this man happens to be one of them. I think this goes along with  a majority of the other time travel ideas in the fact that you can't change big things because they will always happen, but you can change minor things that don't affect the future much.