Mode coupling theory (MCT) is used to model gel formation in mixtures of colloidal particles and nonadsorbing polymer. The polymer induces an effective, short-range attraction among the colloids, which is modeled by a depletion attraction of the Asakura-Oosawa form. This enables the MCT to be solved analytically for dilute systems, leading to a prediction, free of adjustable parameters, of the location of the gel boundary in the phase diagram. For concentrated systems, a simple mapping is suggested that makes a previous theory for Yukawa interactions applicable to colloid-polymer mixtures. The results are compared against Monte Carlo simulations and experiments on model systems. Excellent agreement is observed at high colloid concentrations, where the theory predicts melting of glassy structures on addition of small amounts of polymer. Further addition of polymer causes gelation, in semiquantitative accord with experimental data at moderate to high colloid concentrations. However, at lower concentrations the theory is unable to capture the onset of transient gelation.