Actually, it depends on whether the title is a contraction of the full word or an abbreviation.
Doctor becomes D----r, and needs no period.
Professor becomes Prof. (not Prof----r) and therefore does need a period.
So, technically, it would be 'Dear Mr Jones,' not 'Dear Mr. Jones' in a letter.
It doesn't really matter too much nowadays, like when people use 'less' rather than 'fewer' in lots of circumstances! Even companies advertise saying things like 'now with less calories!' when it really should be 'fewer calories'!