Some of the best razors for men with sensitive skin are electric razors as well as multi-blade razors marketed for men who have sensitive skin. One such razor is the Mach 3 Sensitive.
Electric razors do not shave as closely as hand razors, so, if a hand razor is used, prep prior to shaving and aftershave become very important. Safety razors are also recommended by sites, such as Men's Journal, but can be fairly pricey. With shaving oil and aftershave geared to sensitive skin, a multi-blade razor with a good angle should suffice. Men with sensitive skin should avoid single blade razors and straight razors.