I introduced my nieces and nephew to Grow Games a few years ago after someone at work emailed the link around. I was surprised how much they enjoyed these quirky flash games. They are not your typical kid games where characters go through an obstacle course and shoot at or get shot at. Instead you simply chose objects in various orders and see what kinds of reactions are generated. If you find the optimal order more happens or grows. They are simple yet hard to explain.
The other day my niece reminded me of them and wanted to play one on my computer. We chose Grow Cube. After her visit I found myself still playing. I took this screen capture so I could show her how far I got next time she visits.