This website is another place for young children to play computer games that are easy-to-navigate and perfectly appropriate for children to play on their own.
www.cookie.com/preschool.html will take you to the homepage designed for preschool-aged children. There is one game that might even work with young twos. It is called Learn Numbers. The children are presented with large, bold random numbers. The voice-over (which is that of a child) asks the child to click on a certain number. It then tells the child if s/he is correct. This is simple enough that even the youngest children may be able to identify, point and click. However, many children may still need a grown-up to help them.