Pinterest is a great resource for free wood burning patterns. Although a free account is required to view pins, there are hundreds of user-submitted wood burning patterns available for free. There are also many wood burning tutorials available. Guide Patterns has a list of creative wood burning ideas, from etched wooden spoons to carved cutting boards. They also include a list of free wood burning patterns to print off, from beginner patterns with simple shapes to extremely intricate designs.
Pinterest's wood burning tutorials and patterns are user-submitted, and can therefore sometimes be amateurishly written. LS Irish has an entire section of their website dedicated to wood burning and other pyrography projects, written by author and artist Lora Irish. They have patterns packs as well as in-depth projects with step-by-step instructions. They provide instructions on how to burn animal fur and hair, wood grain, human faces, and other fun doodle patterns.
Woodworker's workshop has a very large list of wood burning patterns with a lot of options. Their options are mostly simple ones, consisting of cartoon characters and holiday pictures with simple lines and shapes. Their images mostly originate from coloring pages and are suitable for carving or wood burning. All of their images can be printed directly from their website.