This paper presents a method for simultaneously determining multiple trajectories of single molecules from sequential fluorescence images in the presence of photoblinking. The tracking algorithm is computationally nondemanding and does not assume a model for molecular motion, which allows one to determine correct trajectories even when a distribution of movement speeds is present. We applied the developed procedure to the important problem of monitoring surface motion of single molecules under ambient conditions. By limiting the laser exposure using sample scanning confocal microscopy, long-time trajectories have been extracted without the use of oxygen scavengers for single fluorescent molecules. Comparison of the experimental results to simulations showed that the smallest diffusion constants extracted from the trajectories are limited by detector shot noise giving error in locating the positions of the individual molecules. The simulations together with the single molecule trajectories and distributions of diffusion constants allowed us therefore to distinguish between mobile and immobile molecules. Because the analysis algorithm only requires a time series of images, the procedure presented here can be used in conjunction with various imaging methodologies to study a wide range of diffusion processes.