Gable / Cross Gabled
Just about the most common roof type is the gable roof. The shape on children’s drawings of houses and on the building pieces in the game of Monopoly, the gable roof is seen everywhere and just about every culture. A cross gabled roof has additional ridge lines perpendicular to the main ridge line.
Hip/ Cross Hipped
The hip roof is another simply formed and easily built roof that efficiently sheds water. But unlike the gable roof, this roof eliminates large expanses of wall on the exterior. This can reduce the amount of exterior siding or other finish and, therefore, can be a cost-effective option. A cross hipped roof has additional ridge lines perpendicular to the main ridge line.
Gambrel
A gambrel roof has a shallow slope lower in the roof structure followed by a steeper slope high up the face. The advantage of this roof type is that it provides for more interior space under the roof than the gable roof does.
Low Slope / Flat
The low-slope roof isn’t totally flat since some slope is needed to let water drain. Think of this roof as similar to your shower floor. Whether with a center drain or a drain located along the edge, the shower floor (or roof) must be pitched to create positive drainage.
Mansard
A more traditionally styled roof that’s been around for many centuries is the mansard roof. In a sense, this roof is more wall than roof, with its almost vertical sloping sides on all faces of the house. It maximizes interior space on the upper level, which, though called an ‘attic,’ can serve as a living floor.
Butterfly
This roof is shaped like the wings of a butterfly and is like two shed roofs that meet over the house. Used for a more contemporary-styled home, this roof type allows for two tall exterior walls that are opposite each other.
Shed
Starting low and reaching upward, this roof is wonderfully simple to engineer and construct. The shed roof is an ideal roof type for where there’s a big view or lots of sunshine that wants to be taken into the home.
source: familyhandyman.com