Daniel and I are gamer geeks.  Our first memory of spending time together (we met gradually, both being members of a fairly large student organization) is a party where we played Nomic.  We started to hang out together more when I came to the game nights he and his housemates hosted.  Attending a gigantic game convention is one of our default annual activities and sometimes our biggest vacation of the year.  So, of course it's important to us to raise a child who likes to play games!

The most important first step was similar to the first step in raising a child who likes to read: We did not suspend our activity just because we had a baby.  We continued to invite people over for game night and to play an occasional game together, with the baby usually in my lap.  A few particular games became too difficult (like IceTowers, in which everyone plays at once, so pausing to mop up drool can cause you to lose), and our total game time definitely decreased, but we kept it up, and by about 15 months Nicholas was firmly interested in playing our games.  He's 4 years old now, and playing games is again a frequent activity in our home.  

A few months ago, Nicholas announced a new rule for Uno, a card game he was playing competently at 3 years 9 months old, even though the box says "age 7 and up".  Sometimes I wonder who comes up with those age limits.  Are they trying to narrow the market for their product??  I mean, Uno is a game in which you play a card that matches the color and/or the number of the card on top of the stack.  You don't even have to know the names of the numbers or the colors; you just have to be able to tell whether they're the same or different.  Most 3-year-olds and many 2-year-olds can do that.  Despite its simplicity, Uno is a fun game for adults, too.  As we discovered at a family reunion before Nicholas was born, it's a great way to get people of varying ages and interests sitting around a table doing something together.

There are a lot of games that serve that function, and many of them can be played by children much younger than the ages specified on the box.  We've bought very few new games for Nicholas but mainly tried him on the (entire chest of drawers full of) games we already have.  They fall into three categories: fully playable, requires hovering, and requires modification.  Notice I don't say any of them are unplayable.  A young child can find a way to play with anything, if you let him!

Fully Playable Games are the ones Nicholas can play exactly as intended.  Yeah, he might forget that he's supposed to hold the cards in his hand such that the other players can't see them, but he learns the rules and follows them without a lot of prompting or mistakes.

Uno is in this category.  By naming each card as it's played, Nicholas practices number recognition.  He learned the meanings of R and S cards before he could read the words Reverse and Skip.  Understanding how a wild card works is a step toward understanding how variables work in algebra and computer programming.

Candy Land is designed for little kids, and Daniel and I have fond memories of playing it when we were little.  We have Daniel's childhood set, with art much less cloying than the current version.  I remember when that art sucked me into fantasy wanderings through the Gumdrop Mountains, and I still mildly indulge in these daydreams while playing this relatively dull, strategy-free game.  It's ideal for practicing basic game-playing skills like taking turns and obeying the card you've drawn.

Chutes and Ladders/Snakes and Ladders is another chance-based game.  This one was Nick's introduction to rolling a die and moving that number of spaces—a concept I now take for granted, which actually is kind of abstract.  We have a board that simply shows the snakes and the ladders.  I've seen versions that depict a child doing something "good" at the bottom of each ladder and being rewarded at the top, and a child doing something "bad" at the top of each chute and being punished at the bottom.  While that makes the game more interesting ("You broke a vase?  Go back to Square 53!"), some of these versions are pretty extreme, depicting children being whipped with belts and such, so look closely before buying!

Checkers is surprisingly playable, given the abstract setup and the weirdness of moving only diagonally.  By the end of his first game at age 3, Nicholas was able to make several moves in a row without mistakes or reminders.

He's catching on to Chess, according to Daniel, but I haven't tried it since I can't remember all the rules of Chess!

Stadium Checkers is a fun game with complicated parts to move and strategic possibilities for thwarting your opponents as well as achieving your own goals.  The rule that you "name your move" before you touch anything means that you can move more than one marble per turn if you plan ahead.

Memory/Concentration games—where you place all the cards face-down and try to turn up two that match—are great for building spatial memory.  I adored this type of game as a preschooler (and invented Fluxxentration, a similar game with a Fluxx deck, as an adult), but Nicholas isn't into them so much.

Dominoes, whether with pictures or numbers, are fun because the satisfaction of fitting a matching piece into place is easy to achieve, again and again.  I played dominoes alone quite a bit when I was little.

Aquarius is a picture-matching game similar to dominoes but with the added twist that some cards have two pictures, some have four, and some have just one.  Also, players are competing to see who can be the first to connect 7 cards with their "goal element".  Each time I've introduced this game to a child under 6, I've started with just the element cards and played several rounds of "you play a card that matches, and then I'll play a card that matches."  Once they're used to that, I add the goal cards and action cards, and we play the full game. 
UPDATE: Looney Labs released a new edition of Aquarius in August 2009, with new progressive rules for preschoolers, using my input!

Icehouse pyramids have been a favorite toy since Nicholas was just 15 months old.  Yes, they are small and pointy, but if your child has good hand coordination, is non-violent, and is sensible about what to put in his mouth, they are wonderful!  We have a firm rule that if you drop a pyramid on the floor (or, when using the floor as a playing surface, if a pyramid skids out of bounds) you must retrieve it immediately.  Nicholas enjoys stacking and arranging them in many different ways, putting them on his fingertips, etc. 

Games that Require Hovering are the ones Nicholas can play, by the rules, if we tell him what to do at almost every step of the way.  This is not as annoying as it sounds.  All of these are the type of game in which players tend to verbalize what they're doing, to watch what's happening when it's not their turn, and sometimes to speculate aloud about the various choices available for their next move.  Coaching a child adds to the verbiage but not all that much.  At this point, because he can't read, much of the hovering is simply reading aloud the words on his cards.

Fluxx and its variants are exciting because things keep changing.  This also enables people to win without strategizing, which is very encouraging.  I've taught dozens of people to play Fluxx, and with adult novices I find myself coaching, "Okay, draw 4 cards, then play 3 cards," so it's not that much different with little children.  My favorite moment is when a pre-literate child recognizes the symbols on a card well enough to announce, with great triumph, "I play a New Rule: Draw 2!"  Nicholas first took an interest in Fluxx at 2 years 4 months, when I received my new EcoFluxx deck in the mail and he demanded to play.  We played SEVEN games in a row before he lost interest! 

Treehouse is the only pyramid game Nicholas plays, so far.  He's been able to play with hovering since 2 years 6 months.  After several games in a row, he begins to remember what a Swap is and what a Hop is and so on, so that he can make the move as soon as I tell him what the die says, but the next time we play I have to give the explanations all over again.  (He also likes to play Giant Treehouse on a team with me: He rolls the die, and I move the pyramids.)

Chrononauts is a complex card game that many adults find daunting.  Last summer at Origins, somebody asked me for a demo while I was the POD, and as I started to explain that I might not be able to focus because of my kid, Nicholas insisted, "I want to play! I can do it!" so we gave it a whirl.  Yes, I had to tell him what to do on every single move, and he was just playing the most appealing card in his hand rather than attempting to complete his Mission or I.D., but he followed the rules, and his alterations of the Timeline made the game more challenging for the other players.  We've played again since.  He seems to find it interesting enough to be worth playing, even though he always loses.

Carcassonne is a long game whose scoring is so complex that I can't play it without a hoverer or constant looking at the rulebook!  When Nicholas wanted to play it at a party, I figured he'd lose interest quickly...but he played a whole game, not caring much about his score but just wanting a turn to place a tile.  Like me, he is very interested in just playing with the terrain tiles and the meeples, never mind the game.

Games that Require Modification involve rules or strategies that exceed Nick's cognitive abilities at this time.  For example, young children have trouble considering multiple aspects of a thing at once: color and number and shape and pattern are too many different aspects for them to keep straight.  They don't have the mental arithmetic abilities needed to calculate the points they'd score for one move vs. another.

Set is one of my favorite games, but it's impossible for a young child to "look for 3 cards that are all alike or all different on each of these 4 attributes"—what?!  Nicholas prefers to spread out all the cards and group them in various ways.  That's valuable practice in sorting and classifying, which will prepare him for playing the "real" game in a few years.  Many kids don't develop the necessary skills until around 11 years old, but I've met a few kids of 6 or 8 or so who were quite good at Set.
    I once gave a Set deck to some relatives, who wrote to me that they had trouble playing the game because the siblings (ages 8, 11, and 16) varied in their ability to find sets.  Their father solved this problem by giving each of them 2 minutes to look at the cards alone and pick up any sets they could find, laying out 18 cards for the youngest, 15 for the middle, 12 for the oldest—the more cards you have, the greater the odds of finding a set.

Bohnanza was first pitched to me this way: "The goal of the game is to have fun.  The way you have fun is by helping the other players win."  This is by far the best way to approach it, because if you're focused solely on trying to win it yourself, you avoid making trades that help other players, and that means you tend not to get the trades you need.  The mutual-benefit approach makes it ideal for kids who don't understand the rules well enough to keep their hands hidden: Everyone helps each other to maximize the bean harvest.  I do agree with the manufacturer that kids need to be about 10 to comprehend the rules on their own.
    For my 4-year-old, I make these modifications to the rules: He doesn't have to keep the cards in his hand in order; he must plant one bean at the beginning of his turn and may choose to plant two beans, but he gets to choose from among the beans in his hand.  (I do keep my own hand in order.)  For all players, I allow plowing up a field of one bean to plant a different variety, ignoring the rule that you must harvest your multi-bean field if you have one; that's a complicated rule and adds a lot of disappointment to the game.

The Labyrinth card game from Ravensburger (until I looked for a link, I didn't realize that they make 5 other variants of this game) involves laying out tiles to form dungeon passageways in which you search for treasures.  I've played according to the rules with adults several times, but the game didn't really grab me . . . I just wanted to play with the tiles!  What Nicholas likes to do with Labyrinth is take turns placing tiles to connect the dragons to the treasures; whenever a dragon is newly able to get to a treasure, he traces its path through the maze with his finger, roaring, "I'm going to get that emerald!" or whatever it is.

Other modification ideas are in my previous article, and I expect to come back and add games to this one later!