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.
cooking.stackexchange.com/users/104/J Wynia
Full fat milk soothes the burn.
cooking.stackexchange.com/users/403/Iuls
Aside from Milk or fatty drinks as an option, there are two other good options: Hot tea or hot coffee.
(Hot water will modestly dissolve oils to an extent and it will also make any saturated fats holding the pepper oils more liquid again.)
Anything alcoholic.
The more potent, the better.
Alcohol is both attracted to water and oils, so it will dissolve the pepper oils and then mix with the water and wash it down your throat.
Beer works well, but wine or a mixed drink will do you better.
Plus you'll be happier after a few drinks.
Combining all 3 options, I think a hot coffee with Baileys would probably do you best .
(Hot, fatty, and alcoholic!)
cooking.stackexchange.com/users/1618/Pretzel
Personally, I find that beer does the job (or maybe I just forget the heat).
cooking.stackexchange.com/users/1753/Tim Almond
Here's some culture-specific answers: If the hot and spicy foot you're eating is Turkish, take the dairy approach.
Nothing is better than ayran .
It's a traditional drink of yoghurt with water, sometimes a bit of salt too.
If you're in Turkey many cheap places even have specially priced offers of a spicy meal and a drink of ayran.
If it's spicy Korean food you're eating, dairy products are not traditional at all.
Instead my Korean friends suggest the alcohol approach.
The standard strong Korean alcohol, available at just about every restaurant, is soju (Korean 소주).
It's similar to vodka though not as strong and a little sweeter.
cooking.stackexchange.com/users/6231/hippietrail
Mountain Dew.
most sodas don't work well, though some say sugar helps, but mountain dew specifically has brominated vegetable oil as a bridge molecule to dissolve the oil based food color that gives it that distinct yellow hue.
the same bridge molecule helps dissolve capsicum in water to wash it away. never found anything that works as well.
cooking.stackexchange.com/users/77377/mike harkleroad
Dairy products like milk, cheese, yogurt are very good at relieving spiciness.
Bread also is very good.
Avoid watery items which don't actually help, and can often make it feel worse because it helps spread the spiciness around
cooking.stackexchange.com/users/1675/Manako
Suck on a lemon(Or a Lime).
Just like the others say, water doesn't work.
Fatty or greasy things do help.
Also, for some reason very sour foods, such as pure lemon juice can provide some relief (Though you may prefer milk or beer).
cooking.stackexchange.com/users/1355/Andres
In my opinion gargling warm water works better than milk.
Yes it would burn a bit more at first but you'll then realize it's literally almost instant relief.
I've tried all approach and gargle warm water and spitting it out works better.
Though I use water that's a bit hotter than warm.
cooking.stackexchange.com/users/43190/Wiindii
Say, for example, I eat a very spicy jalapeno and I have a burning sensation in my mouth and throat.  Are there any foods or drinks to wash that away?
How can I wash down spicy food?
cooking.stackexchange.com
<spicy-hot>
cooking.stackexchange.com/questions/4403
cooking.stackexchange.com/users/1317/Corey
A common recommendation is full-fat milk, cream or other dairy products. Gargling with warm water or sucking on a lemon or lime can also help, although most soft drinks are not effective. Bread can absorb some of the spiciness, and alcohol dissolves capsaicin so beer and other drinks can also help.  The most common solution is a fatty dairy product or alcohol. In addition to this, you can also try bread, warm water or lemon juice.
Gargling warm water works well. The most common solution is full-fat milk, cream or yogurt. Alcohol is a good remedy. Mountain dew soda contains a vegetable oil that works well. Eat a slice of bread. The acid in citrus fruits is a good remedy.