Do modern trains still require brakemen?

No, not in the classic definition of a man who walks from car to car to apply the brakes.

Modern trains have computer monitored air brakes which apply brakes through an air line connected from the front locomotive to the rear of the train. The air brakes are powered by air compressors on the locomotives that are driven by the engine itself. Air applied removes the brakes, removing the air from the line will apply the brakes as a fail safe. This system was originally thought up and put into action by the Westinghouse Air Brake Company (WABCO). It has been since improved and has been the primary braking method for trains since it was patented in 1868. Modern trains now even have dynamic braking of their electrical motors to slow them down as well. Dynamic braking is a method of connecting an electrical motor so that it acts as a generator and drives power to a grid of resistors that dissipate the power of the motor through heat. This, in turn, fights the motor and slows it down. This type of braking is used to precision control train braking/slowing and to assist in speed control in hilly and mountain terrain without using air braking.

You could be a brakeman for the railroads long after walking from car to car to apply brakes was obsolete. Being a brakeman then was similar to being a conductor but with different duties.