A charming little example of neural nets in action, and why they took the AI world by storm not some years ago. In this little example, we have actual optical character recognition (though digits only) using neural networks. This belongs as an example of Connectionist AI.

The ALICE Chatbot uses something called AIML to understand human speech, in a sense. Though better than Eliza, it's still not that hard to confuse it. This belongs as an example of Symbolic AI.

A* pathfinding algorithm, this is used in basically all games where terrain is traversed (in one incarnation or another). This is a basic example, with only one type of agent crossing. This belongs as an example of Game AI

There is a LOT of material on the web about Conway's Game of Life. This is the classic example of cellular automata, where simple rules create emergent behavior. Fascinating, really, that those objects you see writhing are objects like us, made up of smaller, simple pieces. This life has aging cells. This belongs as an example of Classic AI.