One of the earliest chemical tests was the flame test. It was known that a flame will burn different colors depending on the chemicals present long before we had the theory to explain it. When lithium is present, for example, a flame will burn bright red. Barium will burn green. To understand why we needed to first develop quantum mechanics. An electron is excited (its energy increases) by a flame. After staying in an excited state for some time the electron will eventually relax. When it does it releases a photon. The energy, and therefore color, of the photon depends on the element involved. This simple test can therefore tell us a great deal of information about what the chemical make-up of a solution is.
The modern application is, of course, fireworks. When fireworks are made they are stuffed with different chemical elements. Each element giving a distinct color. So tonight, when you see fireworks don't just say "Ooohh....Ahhhh" say "Oooohhh copper....Ahhh...sodium".
Here's a list of the chemicals used for fireworks:
Red: strontium or lithium salts
Orange: calcium salts
Yellow: sodium sals
Green: barium salts
Blue: copper salts
Purple: mixture of strontium (red) and copper (blue) salts
White: magnesium or aluminum
And this great video about what makes fireworks "pop"