So let us imagine that you have a small child whom you wish to introduce to boardgames, and the having read our rant on Candyland you can't face spending time dealing with so saccharine and brain-dead a system. Are there alternatives?
Certainly, and here's one.
3D Labyrinth's board shows a dungeon maze; the center part of the maze can slide to left and right, changing how the corridors of the maze interconnect with each other. At various parts of the maze are images in a fantasy theme (magic wand, black cat, etc.), and the game's cards portray the same images. Each player begins at a corner position. On your turn, you draw a card. You must try to find a path from your current position to the location bearing the same image as the card you just drew, and you may shift the moving portion of the maze before you do so (but not in the middle of a move). If you can get to the destination, you keep the card; otherwise, the next player does not draw a card, but tries to get to the same location to earn that card. At the end of the game, the player with the most cards wins.
Now, in practice, 3-D Labyrinth is just as luck-dependent as Candyland; a location is either reachable or not on one turn, and you have no control over that. The player who is lucky, in terms of drawing cards he or she can easily reach more often than opponents, will win. But as I noted in the Candyland review, having a luck-dependent outcome is not in itself a bad thing in a game played by a mixture of small children and adults; it puts all players on an even plane.
And while there's no strategy by which you can increase or decrease your chance of winning, this is not the same thing as saying that no reasoning is required. You have to think about how the corridors can interconnect, and work to find a path that will achieve your objective. Thus, there is an element of spatial reasoning to play. Your kid might actually learn something, in other words.
Too, the theme of the game is not noxiously consumerist.
3-D Labyrinth is also the simplest in Ravensburger's Labyrinth series (Junior Labyrinth, The aMAZEing Labyrinth and Master Labyrinth), each of which adds strategic elements to the game, with recommended ages increasing for each; it can thus serve as a gateway to deeper exploration of strategic play. The final game in the series, in fact, is one that adults may play with enjoyment.
A Good All-Ages SKILL-Based Game
Greg:
If you are looking for a good all-ages skill-based game, I highly recommend Gulo Gulo. The theme is a little weird (you are a wolverine stealing eggs from a vulture's swamp-nest in order to rescue your baby wolverine from the vulture who kidnapped it because you were stealing the vulture's eggs, or something like that), but the game play is interesting. In order to progress towards the goal, you flip a new tile (or choose an existing one in play) and then need to select that colour egg from a wooden bowl. There is an egg-on-a-stick standing upright in the eggs, and if you knock it over, you move backwards instead of forwards. The sizes of the eggs are such that it is easy for kids with their little fingers to get out of the bowl, but not so easy for adults.
My 4-year-old loves playing it, and I don't mind either.
Chateau Roquefort
Another good kid's game with tile sliding and a 3D element is Chateau Roquefort (aka Burg Appenzell in Europe). Bonus: Cute little mice figures!
http://boardgamegeek.com/boardgame/28089
Other Games
As someone who loves games, I'm always thinking about introducing new people to my hobby.
When I went to meet my younger cousin for the first time (he was 5 at the time), I brought along the game Lost Cities. He had a pretty easy time grasping at the basic concepts of the game, and with a little help (ok, I will admit, I straight up told him) he began to understand the dynamics of strategically drawing and discarding cards.
Some other games that work pretty well with younger kids are Carcasonne and Ticket to Ride. When I play Carcasonne with them, however, I always ignore farm bonuses, leaving only Monasteries, Castles, and Roads to deal with.