Rim (coin), the sharp circular (or otherwise shaped) edge which surrounds the coin design
Rim (craters), the part of a crater that extends above the height of the local surface
Rim (firearms), a projection machined into the bottom of a firearms cartridge
Rim (novel), by Alexander Besher
Rim (wheel), the outer part of a wheel on which the tire is mounted.
Rim (basketball), part of equipment for basketball
Breakaway rim, a specialized rim capable of sustaining forceful dunks