Dogs need physical and mental exercise just like we do. Training is important, and is its own form of enrichment, but there are tons of other things you can do to exercise the mind of your canine friend. Make them work for their food like they do in nature with food-stuffed toys and puzzles. Games that involve nose work like “find it”, and games like Tug (with rules), Hide & Seek and organized Dog Sports are all great ways to work with your dog.
Read this great article on ASPCA about enriching your dog’s life: http://www.aspcabehavior.org/articles/65/Enriching-Your-Dogs-Life.aspx