Look at the architectural drawings of the building and identify the grid that the building supports are arranged on. Structural grids are drawn in lines that alternate a long dash and a dot, with a circular capping on one end of the line. Any beams that fall within the structural lines are more than likely of the supportive variety.
Determine how the beam would distribute the load it may be carrying by looking for columns or arches that would distribute the weight down from the beam toward the foundation of the structure. If the beam ends in a finished wall, you can use a stud finder to seek out wall studs behind finishing materials. If there is no readily apparent way for the beam to distribute a load to the ground then it is likely decorative.
Consider the size and material of the beam. If the beam is particularly small for the structure, or it is made of a weak material, then it is likely supportive. If the beam is part of a steel frame, or is made of a particularly thick piece of wood, then it is likely structural and providing support to the building.
Consult the opinion of an expert such as a licensed architect, structural engineer, or general contractor if you have any doubts at all about the beam before attempting to remove or alter it.