My 3-year-old has never been very good at playing by himself, but I also realize many kids this age are not. So I play with him.
We create environments in which we play farm, zoo, kitchen, construction site, etc. I am a kid at heart myself, so I have large reserves of imagination that I am trying to imprint on my own kids. I believe in the Waldorf-style of play, so many of his toys are open-ended, which is why I try to teach him about all his toys' possibilities.
But when he is down in the play room by himself or with his 16-month-old brother, all he does is dump everything out of the baskets onto the floor. He pulls all the books off the shelves. In minutes everything is trashed. It's infuriating.
He's always been a dumper. But I hoped by this age he would actually be PLAYING with his toys.