An investigation is made of the merits of various emission-line intensity ratios for classifying the spectra of extragalactic objects. It is shown empirically that several combinations of easily-measured lines can be used to separate objects into one of four categories according to the principal excitation mechanism: normal H II regions, planetary nebulae, objects photoionized by a power-law continuum, and objects excited by shock-wave heating. A two-dimensional quantitative classification scheme is suggested.