Cantilevers are widely found in construction, notably in bridges and balconies. Frank Lloyd Wright's Fallingwater used a cantilever to project the large balcony out into "free space". A less obvious example are the common radio towers, which resist being blown over by the wind through a cantilever at their base; the ground below must be "twisted" for the tower to fall over.
Another common use of the cantilever is in aircraft design. Early aircraft wings bore their loads by building two (or more) wings, and bracing them with wires. They were similar to cable-stayed bridges in some aspects, the wings on each side of the plane were braced with crossed wires both along their length, so they would stay parallel, as well as front-to-back to resist twisting. The cables generated considerable drag however, and there was constant experimentation on ways to eliminate them.
The most successful was the cantilever. A single large beam, referred to as the spar, runs through the wing, and often right through the aircraft. Looking at a plane from the front, the wings are both trying to rotate up at the tips, a force that is resisted either by mounting the two spars to each other (each one is twisting in the opposite direction) or to a strong box-like structure in the middle.
Cantilever wings require a much heavier spar than would otherwise be needed in cable-stayed designs. However as the size of aircraft grew, this additional weight dropped in comparison to the overall weight, as well as the growing weight of the cables needed to brace larger wings. Eventually a line was crossed in the 1920s, and designs increasingly turned to the cantilever design. By the 1940s almost all aircraft used the cantilever exclusively, even on smaller surfaces such as the horizontal stabilizer.
See also: engineering mechanics, statics, and Moment (physics)