Those do sound like very troubling thoughts, Joe90...and it is good to be very cautious when you're out walking alone, especially at night. But, as the others have said, I think people being beheaded is a somewhat rare occurrence.
However, it might help you feel better if you carried something with you that you could use in self-defense, if you did run into trouble. A small discreet knife could work, as others have suggested, or you could try carrying mace or pepper spray in a plastic cannister that attaches to your keys with a key clip. I don't think you can take it with you on airplanes, though - just to let you know, if you do decide to go that route.
I have a whistle attached to my keys...it's supposed to alert people that one is in trouble and needs help, but I think it can also serve the purpose of catching a potential assailant completely off guard and make him/her leave a person alone.
Another means of self-defense that I've heard about is these keychains:

...they look like ordinary cat keychains, but can be used as handheld weapons if necessary.
Carrying something with you might help relieve your anxiety some. Hope this helps. 
_________________
I wish Sterling Holloway narrated my life.
"IT'S NOT FAIR!" "Life isn't fair, Calvin." "I know, but why isn't it ever unfair in MY favor?" ~ from Calvin and Hobbes