I think negative lift is where high pressure forms on the top of the wing instead of the bottom. I know that Indy cars use negative lift and some sports cars do, but do any aircraft exist that use negative lift and why do they use negative lift?
A lot of aircraft generate negative lift- not in the wings, but in the tail plane. This is used for stability. Consider a trimmed aircraft as shown below:
Image from grc.nasa.gov
On most aircraft, the center of gravity (through which weight acts) of the airplane is located near the center of pressure (through which lift acts) of the wing. If the center of presure of the wing is aft of the center of gravity, its lift produces a counter-clockwise rotation about the cg. A positive lift force from the tail produces a counter-clockwise rotation about the cg.
To trim the aircraft (i.e. no rotation about c.g), it is necessary to balance the torques produced by the wing and the tail. But since both rotations are counter-clockwise, it is impossible to balance the two rotations to produce no rotation. However, if the tail lift is negative it then produces a clockwise rotation about the cg which can balance the wing rotation. For this reason, the tailplane is designed to produce a negative lift.
Text from Trimmed aircraft- slightly modified.
Yes. Most airplanes have the centre of mass forward of the centre of lift of the main wing(s). This would make the airplane "tip over" forwards, so the tailplane is an upside-down wing, and provides negative lift sufficient to balance the airplane. This is a conventional arrangement. On some, the "car spoiler" shape of the tailplane, with the flat side on top and the cambered side underneath, is very obvious.
Short Answer: Yes
Long Answer: Well, partially....You see, lift is generated not only at the wings but also at the tail. The aircraft's tail has an elevator and a rudder (most single engine planes) by way of control structures. The pitching motion of the airplane is caused by altering the elevator's shape. The nose stays where it is (in the vertical plane) when the lift at the wings is balanced by that at the tail. However, when the lift at the tail increases the nose starts dropping. Similarly, when the lift at the tail decreases, the nose rises up. You could call the increased downward at the tail 'negative-lift'.
I hope that answered your question. If you are patient enough, try reading this chapter from the Pilot's Handbook of Aeronautical Knowledge. It is the same book I used for my pilot's license.