High-resolution scanning-tunneling-microscope (STM) topographic images of vacuum-deposited Ag films are reported. Films were formed and imaged at 100 and 300 K. Images of films deposited at 300 K, annealed to 560 K, and then returned to 300 K are also presented. The topographic surfaces of the low-temperature films are found to be self-affine fractals with a local Hausdorff-Besicovitch dimension D=2.5. The low-temperature films exhibit intense surface-enhanced Raman spectra (SERS). Films deposited at 300 K do not possess significant fractal character and are not SERS active. We show that the apparent local fractal dimension obtained by analyzing STM topographic images depends critically on the algorithm used. Three such methods (cube counting, triangulation, and power spectrum analysis) are assessed. A method is proposed for obtaining reliable fractal dimensions by analyzing the experimental STM topographic images using several algorithms and comparing the results to a calibration curve generated by applying the same algorithms to simulated fractal surfaces of known Hausdorff-Besicovitch dimension.