As you all know, Owen is a very smart, very energetic dog so we have to keep him busy (see my "agility" post for more on keeping a dog busy with activities). About 6 months ago, on a rainy day, I got him his first puzzle toy/brain game. I brought it home and let him try it out and it didn't take him long to figure out how to get the treats! The first one I got him has drawers that he has to slide out to get the treats (blue and green "bone-shaped" one in the picture of the toys, below).
Since that time, I have gotten him/made him several other puzzles/brain games (all pictured below). These toys are GREAT if you have a dog that needs something to do (and what dog doesn't?) to keep him/her busy. They can be bought at most pet stores. They CAN be expensive, but they don't have to be! Most of Owen's were bought when they were on sale and were less than $5/each! You can also make a simple puzzle with a cupcake tin (or, for small dogs, an ice cube tray) and some tennis balls (pictured).
I frequently feed Owen his meals in these toys instead of his bowl because these make him work for his food and also slow him down (he eats SUPER fast!). Other types of "puzzle" for dogs include the "Kong" type toys, feeder balls, etc. (Owen has several of these too but these are easier and are more suited for treats than full meals).
If you want to keep your dog busy and stimulated mentally, get a puzzle toy for him/her and watch him/her solve it!