The general theory of coupled molecular dipoles is applied to the vibrational spectra of interacting molecules on surfaces. Both classical and quantum-mechanical analyses are presented for the infrared-absorption spectrum. Asymmetric (Fano-effect) line shapes are derived for coupled molecules that interact with electron-hole pairs or optical phonons in the substrate. A very general intensity sum rule is derived which may be useful in constructing theoretical models to explain experimental data. The sum rule may aid in assessing the relative importance to electrodynamic coupling effects, chemical effects, and electromagnetic-field-enhancement effects.