Do any aircraft out there 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.