AFF | Awesome Fun Facts

 
Great question and only something that relatively recently has been given a satisfactory answer not based on conjecture, thanks to one Dr. Tonya Coffey of Appalachian State University and some of her physics students.  Dr. Coffey decided to do a study on this very phenomenon after being slightly unsatisfied with MythBusters’ explanation of the phenomenon.  Thus, she did a research project and wrote a paper with her results, later published in the American Journal of Physics, June 2008.
I’ll try not to get too sciency in this answer, as I’ve found most people aren’t big fans of that, but I’ll still try to give a good detailed answer anyways.  If you want a much more technical and formally written response, you can check out Dr. Coffey’s definitive research paper on the subject here.
To start, it should be noted that it’s not just Diet Coke and Mentos that “react”; other carbonated beverages will also readily respond to the addition of Mentos.  The very high level gist of what’s going on here between the Mentos and the Diet Coke is that ingredients in the Mentos/Coke and, more importantly, the structure of the Mentos allows carbon dioxide bubbles to form extremely rapidly; when this happens fast enough, you get a nice Diet Coke fountain.
More specifically, Mentos has thousands of small pores on its surface disrupting the polar attractions between the water molecules, creating thousands of ideal nucleation sites for the gas molecules to congregate. (Wait, don’t glaze over yet, read on!)  So in non-sciency terms, basically, this porous surface creates a lot of bubble growth sites, allowing the carbon dioxide bubbles to rapidly form on the surface of the Mentos.  If you use a smooth surfaced Mentos, you won’t get nearly the reaction. The buoyancy of the bubbles and their growth in size will eventually cause the bubbles to leave the nucleation site and rise to the surface of the soda.  Bubbles will continue to form on the porous surface and the process will repeat, creating a nice foamy result.
In addition to that, the gum arabic / gelatin ingredients of the Mentos, combined with the potassium benzoate, sugar or (potentially) aspartame, in Diet sodas, also help in this process.  In these cases, the ingredients end up lowering the surface tension of the liquid, allowing for even more rapid bubble growth on the porous surface of the Mentos- higher surface tension = more difficult environment for bubbles to form.  (For your reference, compounds like gum arabic that lower surface tension are called “surfactants”).
As to why diet sodas like Diet Coke produce such a bigger reaction, it’s because aspartame lowers the surface tension of the liquid much more than sugar or corn syrup will.  You can also increase the effect by adding more surfactants to the soda when you add the Mentos, like adding a mixture of dishwasher soap and water.
Another factor contributing to the size of the geyser is how rapidly the object causing the foaming sinks in the soda.  The faster it sinks, the faster the reaction can happen, and faster reaction =  bigger geyser; slower reaction may release the same amount of foam overall, but also a much smaller geyser.  This is another reason Mentos works so much better than other similar confectioneries.  Mentos are fairly dense objects and so tend to sink rapidly in the soda.  If you crush the Mentos, so it doesn’t sink much at all, you won’t get nearly the dramatic reaction.
Yet another factor that can affect the size of the Mentos / Coke geyser is the temperature of the soda itself. The higher the temperature, the bigger the geyser due to gases being less soluble in liquids with a higher temperature.  So, basically, they are more “ready” to escape the liquid, so when  you drop the Mentos in, the reaction happens faster.
Note that while caffeine is often cited as something that will increase the explosive reaction with the soda, this is not actually the case, at least not given the relatively small amount of caffeine found in a typical 2-liter bottle of soda generally used for these sorts of Diet Coke and Mentos reactions.  Now, if you add enough caffeine, you will see a difference, but the levels required here to see a significant difference are on the order of the amount that would kill you if you actually consumed the beverage, so obviously not anywhere close to the amount of caffeine in Diet Coke or other such beverages.
You’ll also sometimes read that the acidity of the soda is a major factor in the resulting geyser.  This is not the case either.  In fact, the level of acidity in the Coke before and after the Mentos geyser does not change, negating the possibility of an acid-based reaction (though you can make such an acid based reaction using baking soda).

Bonus Facts:

• While you’ll sometimes hear an urban legend that people have died from drinking Diet Coke and eating Mentos, to date there has not been a single documented instance of this ever happening.  This is likely for two reasons.  First, the act of drinking soda releases quite a bit of the carbonation in it, limiting the possible effect.  Second, even if one did get a strong reaction to eating and drinking Mentos and Diet Coke at the same time, you’d likely just quickly vomit up the foam, which there have been numerous recorded instances of.
• As an aside, while I personally have never tried drinking Diet Coke and eating Mentos, I have had a similar experience after taking a new kind of  multivitamin I’d not tried before, combined with drinking a 16 ounce container of Dr. Pepper.  Within a couple minutes of taking the vitamin (after eating and consuming the Dr. Pepper), I noticed I started to feel like I was going to throw up.  I had not at that point thrown up in about 15 years, so this was bizarre.  To keep my streak alive, I attempted, vainly, to keep the contents of my stomach down.  Ultimately, the pressure became too much and I threw up a ton of foam (red, like the multivitamin coating).  It seems likely that the surface of this vitamin must have been porous and it did most likely also contain at the least the gum arabic.  As I had not chewed it obviously before swallowing, it found its way to the still somewhat carbonated liquid (although much less so having drunk it) and produced enough foam to overfill my already somewhat full stomach from dinner.  So let that be a lesson to you.  Certain types of multivitamins and soda also produce a nice foamy reaction.  I’ve also noticed that if you suck off the chocolate of a Snickers bar and then chew it, and swallow, then very quickly afterwards drink some soda, you’ll also get a nice foamy effect in your mouth.  Science!
• The current world record for more Mentos / carbonated beverage geysers to be set off simultaneously happened on October 17, 2010 and included 2,865 such geysers.
• The name “Coca-Cola” was suggested by the creator of Coke, Dr. John Pemberton’s, bookkeeper, Frank Robinson, stemming from the two key ingredients: extracts from the coca leaf and kola nut. Robinson was also the one to first pen the now classic cursive “Coca-Cola” logo.
• While there were initially different versions of Coca-Cola being sold (depending on the manufacturer, of which there were three primary businesses Pemberton had sold the formula to), all the versions contained cocaine, with some estimates of up to nine milligrams of cocaine per serving.  However, Asa Candler, who eventually finagled exclusive rights to Coca-Cola, claimed that his formulation included only around 1/10 the original formula amount of cocaine and by 1903 he removed cocaine from Coca-Cola by using “spent” coca leaves leftover from the cocaine extraction process.  This still resulted in Coca-Cola having trace amounts of cocaine though.  They’ve since got around this by using cocaine-free coca leaf extract.  The company that prepares this extract, Stepan Company in Maywood, New Jersey, also legally makes cocaine for medicinal purposes.
• The term “soda-pop” was a moniker given to carbonated beverages due to the fact that people thought the bubbles were produced from soda (sodium bicarbonate), as with certain other products that were popular at that time.  A more correct moniker would have been “carbonated-pop”.
• The “pop” part of the term came about in the early 19th century, with the first documented reference in 1812 in a letter written by English poet Robert Southey; in this letter he also explains the term’s origin: “Called on A. Harrison and found he was at Carlisle, but that we were expected to supper; excused ourselves on the necessity of eating at the inn; supped there upon trout and roast foul, drank some most admirable cyder, and a new manufactory of a nectar, between soda-water and ginger-beer, and called pop, because ‘pop goes the cork’ when it is drawn, and pop you would go off too, if you drank too much of it.”
• While in the beginning carbonation was added to drinks because it was thought it was beneficial to the human body, today carbonation is added for very different reasons, namely, taste and shelf life.  Carbonating beverages, introducing CO2 into the drink mix under pressure, makes the drink slightly more acidic (carbonic acid), which serves to sharpen the flavor and produces a slight burning sensation.  It also functions as a preservative, which increase the shelf life of the beverage.