We consider experimentally and theoretically the effect of the thickness on the critical current density ital Jsub ital c of superconducting films. In order to eliminate possible contributions from intrinsic pinning, our measurements of ital Jsub ital c(ital cphi) as a function of the amplitude and orientation of the magnetic field bold H with respect to the film plane were performed on isotropic Nb-Ti films having thicknesses ital d ranging from lambda/4 to 4lambda, where lambda is the London penetration depth, and bold Hperpendicularbold J. The angular dependent ital Jsub ital c(ital cphi) has a sharp peak for bold H parallel to the film surface, similar to that observed for high-ital Tsub ital c films. The amplitude of the peak increases as ital d decreases and reaches 20--30 % of the depairing current density (ital Jsub ital d) for the lambda/2 film. The ratio of ital Jsub ital c values for parallel (ital Jsub ital cparallel) and perpendicular (ital Jsub ital cperpendicular) film orientation increases as ital d decreases, so that ital Jsub ital cparallelmuch ltital Jsub ital cperpendicular for the 4lambda film and ital Jsub ital cparallelmuch gtital Jsub ital cperpendicular for the lambda/4 film, the crossover occurring at ital dapprox2lambda. A proposed interpretation of these results is based on our calculations of the vortex behavior in thin (ital dmuch ltlambda) films, which give analytical formulas for the field distribution around a fluxon, the lower critical field, ital Hsub ital c1, the surface barrier, and the vortex-vortex interaction potential.