As a redhead, I naturally have extremely fair skin so I've endured many burns from mild to extremely severe. The best thing for me is to run a lukewarm bath and float some teabags in it. (I usually use between 5 to 8). Let them steep for a few minutes then get in. The tea takes the sting right out of the burn!
Sunburn comment: Easier and more efficient is to just boil 1/2 cup water and steep a tea bag in it for 5 minutes or so. Add 2-3 ice cubes and using a cotton ball or even the tea bag (until it breaks) apply directly to the sunburn and allow it to dry on the skin.