There are a lot of weird and wonderful autonomous actions that can occur.
Toddlers can play in the toilet, rock to music, eat sand, sometimes even break out of their cribs.
Animals can sing along to music:
http://i.imgur.com/BOQ0h6m.png
Even adults can do some unexpected things such as playing in the bathtub or washing themself in the kitchen sink:
http://i.imgur.com/w01ebtO.jpg
And then you get the neighbours stopping by to steal a yard gnome or the newspaper.
http://i.imgur.com/DxmmBXQ.jpg
I did discover something new (for me) just yesterday. Sims can juggle cups from the coffee machine and if you get another sim to join in they will juggle the cups between them.