Just came across this list and, on the assumption that others will do the same while researching games for their children, thought I'd add one or two. First Orchard is an excellent first game, with great components. Manufacturer suggests 2+, users suggest 2-6 years.
Our boys were playing this as early as 2 years old. Teaches great turn taking, and color recognition, and die rolling. Two color sided die determine the movement of the snails in the race. No one wins our looses, everyone moves all snials on their turn. Children can discuss who they think will come in first as the race continues.
Great wood snail peices. My son always asks for this one.
Like many of the Haba games targeted at the really young audience, several different levels of "play" are recommended, which include reading the poem and pointing things out in the illustrations, freely playing with the parts as toys, and actually playing the game with rules.
A one player game, making pictures by matching large, coloured, plastic buttons to an underlying picture, and plugging them into the see-through board. Lovely Ravensburger pieces, great colour matching practice, dexterity practice for small fingers. Manufacturer recommends 2+, users suggest 2-3.