We discuss the role of the width of a Feshbach resonance for binary and ternary collisions. We show that low-energy few-body observables are universal functions of the resonance width and the scattering length. The effect of narrow resonances is qualitatively different from that of wide resonances revealing novel physics of three-boson collisions. We calculate the rate of three-body recombination to a weakly bound level and the atom-dimer scattering length and discuss implications for experiments on Bose-Einstein condensates and atom-molecule mixtures near Feshbach resonances.