A Gable Roof is most probably the most common of roof shapes. It is when two of the side walls are build-up to the underside of the roof with the roof projecting over the walls. If the walls were to be build up higher than the roof it would be called a Parapet Roof.
A Hipped Roof is when the walls are at the same level with the roof sloping down to all the sides from a middle point, also referred to as the ridge line.
A Dutch Hipped roof is very similar to a Hipped Roof with the hip-apex off-set to the wall creating a cantilever hipped end, however the end are cut-off and the gable wall is build up to create the "Barn Type" look.
The Louvred Hipped roof is also similar to the hipped roof, but the ridge line is extend from the apex and end in a vertical louvred end to allow for ventilation through the roof space.
A Flat Roof is simply what is says, a flat roof. This roof type can be constructed with only loose timber referred to as Rafters or roof trusses can be used if there is enough height available to accommodate a stubbed-truss design.