I presented the emerging list of examples over my blog and several people suggested a few more examples. I will mention them together:
Tom LaGatta proposed to add the percolation model (1854), John Sidles made several suggestions and in particular proposed several examples from Control theory such as the Nyquist criteria, Christian Blatter proposed adding the Peano curve, and Mark Meckes proposed adding the fundamental Banach spaces L_p/l_p and C(K).
Joe Malkevich proposed several basic examples of games in addition to the prisoner dillema dilemma (chicken, chain store game, and centipede) and the Gale-Shapley model of two-sided market model (the model in the famous Gale-Shapley stable marriage theorem). I thought that we should probably add a basic economic model of exchange markets (like the Arrow-Debreu model).
There was also some critique on the classification of examples, and an interesting suggestion By Michael Nielsen that "Distilled and expanded, it could form the basis for an excellent book. Perhaps: 'Examples from the book'." (This refers to Aigner and Ziegler's book "Proofs from the book". (In fact, a similar idea by Ziegler and me have motivated the question itsef.)