Contrary to popular belief, there is no such thing as privacy on the internet. You can click all of the privacy settings that you want, but if there is an image that you would rather not have strangers see, just don't post it. There are software tricks that are designed to keep someone from downloading an image, but believe me, if it's on the internet, someone with a little bit of computer graphics knowledge can get it.
I'm not saying this to make you nervous. I'm saying this because I think sharing images on the internet is wonderful. I myself post public domain images on a Google+ page that I call Phoenix, Arizona Historical Images. And I do it for fun. I love sharing this kind of stuff, and I hate seeing it being locked up somewhere, or thrown in the trash.
Sharing an image on the internet is like giving a gift. Once you've given something away, you have no further control of it, nor should you want control. If I give someone a gift for their birthday, I don't follow them around to see what they do with it. It's no longer mine, that's what a gift is. If it were still mine, it wouldn't be a gift, it would be, I think, "lend-lease". Don't quote me on that, I'm a Graphic Designer, not a lawyer.
If you don't want an image to be taken freely, for example, if it's a sample of original artwork that you created, do a watermark on it. If there is a subtle pattern all over the image, trust me, no graphics person in the world can remove it without making a mess, and besides, they'd have to be a bad guy, and most people aren't. But if it's not, I would recommend not writing "copyright" all over something that is a gift.
A gift can't be stolen from me, as I am giving it freely. And it can be re-gifted, and I hope the images that I post of historic Phoenix will be. If you like them, then I would like to encourage you to share. It's a great feeling.
Photo above: The Westward Ho Hotel and the Phoenix Main Post Office in 1937, Central and Fillmore.