When three particles can form a bound state with (nearly) zero energy,we say that they are at a zero-energy three-body resonance. A prime example of such resonances is three ultracold atoms with large scattering length tuned near a three-body threshold, at which the three-body recombination rate is resonantly enhanced. I show analytical results for the two-body and three-body contacts of such a system within the model of contact interaction. The concept of three-body resonance is however not limited to particles with large scattering length. For a more general three-body resonance, we introduce the "three-body effective range" and illustrate a couple of its applications. These results may also be useful in nuclear physics, since there are three-body nuclear halo states.