Some free beading loom patterns include alphabets, small animals, flowers and symbols and can be found at Shala's Beadwork. Free beading loom patterns are rare, so tips from craft blogs like those found at Abigail's Crafts How-To on creating and converting patterns from other sources make a good alternative.
One alternative to searching for rare free beading patterns is to use graph paper to convert pictures into patterns. While this requires more time than searching, it offers jewelry makers the chance to customize their work.
Another option is to take free knitting patterns, which are both much more common and laid out in a grid just like loom patterns, and use them for beading. A program called KnitPro 2.0 exists that takes image files and converts them into a grid that works for both knitting and loom beading.