Legos were the best, especially growing up in a place with long winters. My kids got my collection and more were added.

Years ago I came into possession of many, many pieces of ~4m long 35x35 mm off-grade building material for the Japanese market, called "turuki". I cut out the knots, planed the resulting pieces down to 33 mm a side, and then cut them into lengths that are multiples of 33 mm, up to 8x. Young children just love to stack these because they can always make their structures come out level. (I think it also helps them learn about integers, but that's getting too geeky.)

My kids and I made up a game. Each person had a turn at selecting a block and stacking it. No verbal communication about intentions was allowed. The idea was to see what would result. Here's an example:

We were obviously on the same page regarding the base for this particular one.