In earlier Blender versions, the "Transform Properties" panel showed the object dimensions (i.e., bounding box: width, height, depth). Now, it just shows location, rotation, and scale.
While CoDEmanX's answer is still correct for Blender 2.8, you have to have the Modeling view mode (bar at the top) selected and be in object mode for the dimensions to appear in the transform panel. User serdar.sanri added this information here, however this question pops up first in the google search, so it might help to find this comment here, too.
As of Blender 3.0, Modelling view is no longer required.