When you see an image hosted on a photo-sharing site that has EXIF information listed with the image it was most likely extracted directly from the image by the software used by the webserver. No one takes the time to type all of that information in, as some people may upload thousands of photos a week or more. That would get quite tedious, so a good number of these photo-sharing sites have support for automatically grabbing EXIF information from the photo.
Having said that, there are multiple ways and numerous softwares to help you to accomplish what you had originally asked. The particular software that I use is called IEXIF and is available from
Opanda. This software allows you to see the EXIF information contained in any image downloaded to your computer from your camera. It also adds the wonderful (and somewhat unique) ability to right click on any photograph in your webbrowser and extract the EXIF information for that image on the fly. This allows you to see the EXIF information for other people's photos who may have them on a webserver that doesn't automatically grab EXIF data from an image.
Another good piece of software that allows reading and exporting EXIF data is Exif Reader by Ryuuji Yoshimoto and is available from his website
here. This program has some of the best support for displaying manufacturer specific information encoded into the EXIF data of any I've been able to find.
Another piece of software that is widely used is Exifer by Friedemann Schmidt which you can download from his website
here. This is part image browser, part EXIF data viewer. This program has support for batch EXIF exports and imports.
Hope that I've helped some...