Facebook has recently launched a way to share the album with public without having to Signin. Every album will have link below this key word Share this album with anyone by sending them this public link. Take a look at this HOW TO for more information.
EDIT: However, for embedding refer this SO which explains how to grant permanent access to your photo albums
Another option is using 8 photo restricted Facebook Photo Badge
Showzey seems to be working on liberating your photos and provides widgets.