Can I introduce myself as Mr?

Is it common to introduce yourself as Mr Jones, e.g. "My name is Mr Jones"? I always thought that it is very unusual to do that (unless you introduce yourself to children, and especially when you are their teacher). Would you do it when introducing yourself to an adult? Or does it depend on where you are from?
Would be great to get answers from native speakers from a number of different English-speaking countries. Thank you!

There's an annoying tendency - well, I think it's annoying - for tradesmen to insist on using Christian names. This seems to me to be unbusiness-like, but I suppose I'm saddled with it. If I had a title, I'd say I'm Dr Smith. Like natkretep, I'd say something like The name's Smith if I were ordering a taxi. If I were being introduced to a circle of friends in a pub, I'd say I'm John. In a more formal situation, I'd say I'm John Smith. I'd even introduce myself just by my surname in an impersonal situation: My name's Smith. I ordered a laptop.
In GB, Mr is almost always a courtesy title only. So awarding yourself the title of Mr is a bit of a solecism - like giving yourself a clap. But it's difficult to avoid it at times.
However, it is also a medical title in GB - one up from Doctor, I believe. So it would be normal for a medical Mr to introduce himself as Mr.