Discreet means on the down low, under the radar, careful, but discrete means individual or detached. They come from the same ultimate source, the Latin discrētus, for separated or distinct, but discreet has taken its own advice and quietly gone its separate way.

Today discreet is to be politely private about something and to be aware of consequences if everyone finds out what you're doing. Be discreet when you eat the lollipop your mom gave you but not your sister, so you don't have to listen to a tantrum. Wealthy people often try to be discreet with their money, because they don't want everyone to know they're rich. When you're trying to be cool, and keep something quiet, you're being discreet:

A source said: "Wayne attracts a lot of attention and the millionaires attracted to the area like to be more discreet." (The Sun) Sound Level: Quiet, with widely spaced tables allowing for discreet conversations. (Business Week)

Discrete remains closer to its roots, meaning individual, detached, separated:

It is far better to think of these as isolated, unpredictable, discrete events. (Salon) Quantum theory is usually thought of as discrete; after all, that's what the word "quantum" connotes. (Scientific American) So last year, when earthquakes were recorded in small, discrete clusters in north central Arkansas, researchers perked up. (New York Times)

Although discreet and discrete have separate (or discrete) meanings, they are often confused. Remember that the "ee's" in discreet hide together in the middle of the word, but the "t" in discrete separates them.