In my experience, for most non-GIS folks, the most commonly used and understood coordinate system is good old Latitude and Longitude, displayed as degrees, minutes, and seconds (DDMMSS.ss). In GIS, it's of course much easier to use decimal degrees (DD.dd), and with the growth of everyday GIS apps like Google Maps, the non-GIS user is much more familiar with decimal degrees these days than they were 10 years ago.
But every now and again, someone brings me a set of coordinates in degrees and decimal minutes. This seems like the worst of both worlds: it can't be used in GIS without a little work, and the format is not immediately obvious to most non-GIS people (many think that it's DDMMSS at first). So why does it exist when we already have decimal degrees, which is easily understood by computers, and degrees-minutes-seconds, which is easily understood by humans?