An effect discovered by (and named after) Henri Marie Coanda in the early twentieth century (he first noticed it in 1910, but spent several decades exploring it before a certain Professor Albert Metral named the effect after him). It essentially states that "a fluid stream which comes in contact with a gently curved solid surface will tend to follow that surface". This can be easily observed by placing a spoon (or other curved surface) under a gently flowing faucet, and noticing how the water bends around the spoon.
The Coanda effect (along with the third law of motion) is primarily responsible for the effectiveness of curved wings (rather then the Bernoulli effect, as is often cited). The curved shape of the wing encourages the air passing over the wing to flow downwards. Thanks to Newton's equal and opposite reactions, this downward momentum must be balanced by an upward force, providing lift for the wing.
Recognizing the Coanda effect makes it possible to design more effective aircraft. Further there are many engineering applications other than flight (almost any technology which deals with fluid flows will experience the Coanda effect).
Coanda first noticed this effect while test piloting a plane of his own construction (the Coanda-1910). He noticed that flames and gases from the exhaust tended to remain close to the fuselage (which meant they were flowing towards him!) rather then spray out behind the plane (he was so excited by this observation that he almost crashed the plane into a wall, or so the story goes).
Henri also proposed that a flying saucer like craft could be constructed based on this principle, though (to the best of my knowledge) only toys (the Coanda Saucers) have thus far been built.