Let's make another attempt to cover a game which is intended for younger players. Happily in the case of Max, we have found an example that's perfect for even fairly young children. As a bonus it's a cooperative game and has a nice elegant system of play.
In the game of Max the players try and move three little animals across the yard and into a tree before Max the cat can catch them. The players control all the animals and Max's actions run automatically. The players start out on a board with a pathway of spaces leading from the house to a tree. The animals (a cute bird, chipmunk, and mouse) start six spaces ahead of the cat. In each turn the players roll a pair of dice. The die rolls will decide whether the animals move, Max moves, or both the animals and Max move. The odds overall favor Max covering more distance and appearing to "catch up" to the bird and her friends.
The players do have some tricks to even the match. One trick is that they have four "cat treats." At four different moments they can offer Max a treat and he has to go back to the start. The animals also have shortcuts they can move across. Each animal has a shortcut specifically for them to use. If Max lands on a shortcut space he Must take it. This leads to the last wrinkle to the game. Max can only go forwards. He can actually hit a shortcut and end up in front of the little creatures. At that point the animals are temporarily safe as they trail behind Max.
I like a lot that Max has to offer. The board and components are small and simple but they get the job done. The game is cooperative so you avoid the winner/loser dichotomy. A thoughtful parent should be able to spin any outcome into something worth congratulating the players over. The concept is simple enough for very young children but there is enough decision making to satisfy older players as well. Possibly the only downside is that in some circumstances one or more cute small animals are going to be caught by the cat. I would just say "oh, the mouse ran away," rather than "Max ate your mouse."
I haven't seen Max in local stores, it may require a special order. I think it has a lot to offer younger players, however, so it's worth the extra effort.
Pros: Cooperative play, good for very young players
Cons: May be difficult to find
Beyond the Basics: It's a pretty simple game so long term replay value is low, at least until your kids get kids of their own...