Is it possible to keep someone from downloading an image from my Web site?
It's certainly possible to secure some of the files on your Web site. The process will vary depending on the Web server platform you (or your ISP) are using, but regardless nearly all Web servers allow you to password-protect certain files or directories and make sure that only certain users get access.
On the other hand, if what you're trying to prevent is people saving the images from your Web pages to their hard discs, then you're out of luck. This is because in order for the browser to display the images that are on your page, the browser must download them to the user's machine. Once there, users can pretty much do anything they want with them, including saving them to their local machine.