The One Place In The United States Where You Get Away With Murder
First and foremost, I am not bringing this up in order to inspire a murder, but I think it's pretty crazy that there is a spot in the U.S. where it would be impossible to prosecute someone for a crime. The place for the perfect crime is in Yellowstone National Park; specifically in the Idaho portion of the park.
There's quite a bit of legal mumbo jumbo that I'll spare you from, but in a nutshell: The courts in Wyoming have jurisdiction over Yellowstone. If a murder was committed in the Idaho section of the park, the defendant could invoke his 6th amendment right to a jury composed of residents of the state in which the crime was committed. So, we would need 12 people who live in Wyoming's jurisdiction and the state of Idaho. There are no such people. In theory - no jury, no trial...no case against the defendant.
Now, before you go making a list of people you're mad at, remember that this is all theoretical. The constitution is pretty easily sidestepped these days, so most likely they would end up finding a way to get you locked up, but at this point in time, there is no way to put someone on trial in this scenario without violating their constitutional rights.