Facebook offers multiple methods to copy and download either your own or someone else's photos. You can download or copy photos individually while viewing the photo, or send a request to Facebook to download all of your Facebook data, which includes your photos.
Using Right-Click Options
From within Facebook's photo viewer, right-clicking an image displays a menu with options to "Copy Image URL" or "Save Image As." The exact wording may differ depending on your Web browser. Copying the image's URL is like copying a line of text -- if you right-click a text box and select "Paste," the URL for the image appears. The Save Image option opens a Windows Explorer window to save the photo to your computer.
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Using the Download Link
When viewing a photo, select "Options," then "Download." Similar to right-clicking and saving an image, this option downloads the photo to your computer.
Downloading Personal Information
You can download all your Facebook data, including photos, by clicking "Download A Copy of My Facebook Data" from Facebook's Settings menu. Select "Start My Archive" and Facebook automatically emails you when your data is ready to download. You can't pick and choose what you download, but the data includes all your currently uploaded photos.
Being Aware of Copyright and Permissions
While you can download or copy any image on Facebook, doing so does not automatically give you rights to the photo. Using the photo elsewhere may infringe on the uploader's copyright to the photo. It's wise and courteous to ask permission before downloading another user's Facebook photo.