Mormon Find has a section on their site that contains several games, both for kids and for older kids (adults like me I guess).
For smaller children there is a match game, which seems pretty simple. I guess it's more about reading and sharing that time with your child. The other children's game is called Noah's Ark. You maneuver the ark back and forth in the water trying to catch the animals (2 of each of course) as they fall from the sky. All the while the water is rising. Not bad, but it was hard to catch the animals as sometimes animals already on the ark would be bounced out as others were caught.
There are also 2 3D maze games. One, Quest of the Plates of Brass, is about finding certain items that Nephi encountered in Jerusalem. They each have a particular letter next to them in the maze. You have to enter the correct letter next to each item at the bottom of the page. In the other maze game, 2000 Stripling Warriors, you have to find Christ in the maze.
Puzzles are also an option on Mormon Find. There are a plethora of jigsaw puzzles that can be done (mostly temple pictures). The concentration game can also be played (what I think of when match game is said).
Lastly, there are some quizzes/trivia based games.
All in all a pretty good place to go find some interesting/different type LDS games that aren't had anywhere else.