When you get right down to it, Coca Cola is a solution of water, sugar, caramel and artificial flavours, preservatives, and lots of carbon dioxide. The latter is the important part. It is added to the cola under pressure at the bottling plant, and it is this gas that makes the drink "carbonated." You can see the carbon dioxide escape in a small rush when a bottle of Coke is opened, and continue to escape in a small-but-steady stream via the little bubbles present throughout the Coke when it is in a glass. This demonstrates that exposed to the open air, but otherwise undisturbed, the carbon dioxide in the Coca Cola wants to escape. The effect can be accelerated with a little outside motivation. For example, everyone knows if you shake a capped bottle of Coke and then open it, the cola spurts out of the lid in a small geyser. This is because the carbon dioxide, excited by the shaking, is making its big escape from the cola. It will do so the moment the cap is removed and the pressure holding it down is released. If a bottle of Coke that has been shaken a great deal is left alone for a few hours, or chilled and left alone for an hour or so, that excitement of the carbon dioxide settles down.
Mentos cause the carbon dioxide to come out of the cola solution so rapidly that the results are explosive. If a small geyser is the result of shaking the bottle, putting a dozen Mentos down the spout is enough to cause a major geyser. There have even been reports of plastic 2 litre bottles of Coke exploding because Mentos were crammed into a bottle that was then capped. The pressure from the carbon dioxide coming out of solution and expanding rapidly overcame the structural limits of the plastic bottle, causing it to burst.
There actually is some debate over why Mentos tablets are so good at this. The Mythbusters of Discovery Channel fame maintain that there is a chemical component to the reaction. Meanwhile Steve Spangler, one of the original 2005 Mentos and Coke experimenters, says it is strictly a physical reaction. The one thing they both agree on is that nucleation is critical to the process. At a microscopic level, a Mint Mentos tablet is heavily pitted and scarred. This provides the perfect place for nucleation, or the mass formation of gas bubbles, to take place. Also, if the Mythbusters are right and there is a chemical part to the reaction, the vastly increased surface area provided by the pits and striations only speed that reaction. Finally, Mentos are heavy and sink right to the bottom, increasing both the speed and scope of the reaction they cause. A spoonful of salt also causes a Coke geyser, but not as substantial as what tablets of salt might, precisely because the small crystals do not fall as far or as rapidly, limiting the reaction amount of carbon dioxide they upset.
The first consideration is that, as demonstrated on Mythbusters, only the Mint Mentos produce the dramatic reaction of a geyser of Coke. That is because the non-mint tablets have a glaze on the surface, which drastically reduces the pitting that makes so much nucleation possible. The second consideration is that artificially-sweetened soft drinks have a lot more carbon dioxide packed into them than sugar or corn syrup-sweetened soft drinks. The result is that Diet Coke has more explosive potential than regular Coke.