How can I wash down spicy food?
The chemical responsible for "the burn" is Capsaicin. The main reason you and everyone else has trouble with the lingering burning sensation is that it's not water soluble (which means it doesn't dissolve in water). So, flooding your mouth with water-based liquids doesn't loosen up those Capsaicin molecules on your tongue and throat. 

Like @Iuls says, the most common and effective relief comes from full-fat milk or cream. That's because, while Capsaicin isn't able to be dissolved by water, it is fat soluble. It's also why more than a few people have been upset that the "milk solution" didn't work, when they tried it with skim milk.

If you're looking for a more "fun" solution, it's worth noting that Capsaicin is also alcohol soluble, which might explain all of that tequila and beer they sell at Mexican restaurants.