Facebook Photo Downloader for Android lets you download photos from your favorite social network.
See a picture you like on Facebook? From the options menu, select Share and then select 1 Click Save. The photo is immediately downloaded to your device's photo gallery into a folder called "Facebook Pics".
Facebook Photo Downloader can download a single photo, but not an entire album. It's easy to use and no special permissions are required. The app integrates well with FB, but user options are limited.