Actually, I suspect that most barbers could, but Ukranian hairdresser Olek Maksakov will cut your hair blindfolded and do a good job of it. Even better: Maksakov usually charges customers for haircuts. But if you agree to let him wear the blindfold, he'll cut your hair for free (he needs the practice).
This is why I ended up with a style that allows me to do it myself most of the time.