Who says you can't take pictures and cut off peoples heads? Ok maybe no one has said this but I set out to do this on purpose occasionally because I think you can really tell a lot about a location or context even with a person with their head cut off in the photo. Sometimes you don't want people to look at the person's face because it will take away from the photo. You don't have to limit youself to removing the head at the edge of photo, instead try removing their head with something in the photo such as an umbrella as seen in the last photo.
Here are a couple photos taken down at Pike Place Market in Seattle, Washington. Next time you're out there taking some fun photos try cutting off some heads!