If you are talking about Lightroom, change the metadata display option to EXIF and the serial number will be included. If you are talking about Bridge, look under Camera Data (Exif) in the right-hand panel.
Thanks Jim, much appreciated; it was Lightroom that I wanted to know about.
It's interesting that this info is easily seen in Lightroom and Bridge in RAW DNG or JPEG, however when you export from DNG to JPG and try to view serial number in the properties on a Windows PC the make and model of the camera can be seen but not the serial number. Diversely, if you export from a RAW to JPEG it is quite the opposite, it is easily seen.
I prefer not to use DNG. It is a standardized raw file format, that's true. But not every computer software company fully supports it. This is probably an issue that you would have to take up with Microsoft.
Added later: This has to be a Microsoft issue, I think. I exported a JPEG from a DNG file, and you are right. The serial number does not display in Windows properties. However, I opened the image in Photoshop and looked at the file info. The serial number and model are in the JPEG file.