About the only way to really secure images on the net is by using flash. The problem is, that's over almost all casual user's heads, and of course you have the issue that not everyone viewing your site may have flash. But, being an avid internet user, flash is the only device I've come across that truly secures images. They may still be accessible through flash, but I've never been able to find a way to save an image in flash, whether through a browser or other program.
Other than that, if it's on the internet, you have to assume that it is accessible and savable to and by anyone. This is especially true on massive public sharing sites, like flickr, versus, for example, this site's forum where you must be a member to see an attached photo, which means it is far less likely to have a random person save it.
The thing is, as pointed out above, in almost all cases people are harmless users - even though they may technically wrongfully obtain or claim your image, most of the time they're merely sharing it with their own friends, adding it to favorites, or something along those lines. They aren't going to try to publish it somewhere or somehow make money from it. The only way to give notice to them and anyone else that it's your image is to watermark it - EXIF is good, but is very easy to get rid of via resaving the image - where as watermarking requires, at minimum, cropping it off of the image.
Point being, even though you can't control your images on the 'net, your actual risks are extremely low.