In a previous comment, ideasman42 explains : stamp options are written into metadata of EXR/JPEG/PNG files.
But I can't find any EXIF information in JPG and PNG files generated by Blender (version 2.78).
Enabling Meta Data in the Render tab does not change anything...
Edit :
After some investigations, I realized that stamp informations are stored in the image file as JPEG markers and not in EXIF format...
Metadata can be displayed with a JPEG utility like jpeginfo :
$ jpeginfo -C untitled.jpg
untitled.jpg 960 x 540 24bit JFIF N 13028
"Blender:File:<untitled>" "Blender:Note:dominique Parisot"
"Blender:Date:2017/08/17 19:46:52" "Blender:Time:00:00:00:01"
"Blender:Frame:001" "Blender:Camera:Camera" "Blender:Scene:Scene"
"Blender:RenderTime:00:00.05"
But they can not be found with an EXIF utility like exiv2 :
$ exiv2 untitled.jpg
File name : untitled.jpg
File size : 13028 Bytes
MIME type : image/jpeg
Image size : 960 x 540
untitled.jpg: No Exif data found in the file
$ exiv2 untitled.jpg File name : untitled.jpg File size : 20692 Bytes MIME type : image/jpeg Image size : 960 x 540 untitled.jpg: No Exif data found in the file
$\endgroup$