How about your average moron with an engineering degree like me?
In Canada, there's a very strict definition for engineer. If you don't have an engineering degree from an accredited university, and a professional designation, you cannot call yourself an engineer. They take it very seriously since it's a regulated profession.
Obviously everyone is free to draw their own lines (outside of Canada at least).
I always thought an engineer was someone who puts scientific or mathematical theory into practice and to solve technical problems. I'm ok with someone giving themselves the title of engineer if they do that for a living. On the other hand, they should not call themselves a "Professional Engineer" without the proper accreditation.
They also drive locomotives, for some reason.