How does the Mentos-Coke explosion work?
It's actually not a chemical reaction, but a physical reaction.  The surface of mentos acts as a nucleation site for the dissolved carbon dioxide in soda, allowing the gas to come out of solution quite rapidly.  This rapid release of gas is what causes the coke geyser.  Despite mentos appearing to have a smooth surface to the naked eye, there are actually a multitude of microscopic crevices, providing a large amount of nucleation sites.  As far as diet coke working better than regular coke, I am unsure (perhaps diet coke has more carbonation?  Or perhaps there are chemicals in diet coke which make it form foam much better than the other sodas).  I always thought that it was the mint vs fruity mentos that made the largest difference (mint seems to have a lot more nucleation sites which explains the larger geyser in comparison to fruity mentos).