A hip roof has four sides that slope up. It is also low-pitched to allow snow and rain to easily run off and features large eaves. A hip roof is more aerodynamic than most gabled roofs, allowing it to better withstand high winds.
The classic gable roof has two slopes forming a ridge or a peak at the top. From either end, the gable looks like the letter A. Gabled roofs must be braced properly to prevent damage or collapse due to high winds. A very triangular roof, the gable allows rain and snow to run off easily.
The Lean-To or Shed Roof is the simplest style, consisting of a single sloping plane with no hips, valleys, or ridges. A single-slope roof is probably lowest in construction cost and time. If a lower-pitched roof is attached against the eave of a steeper pitch, or against a wall, it is usually referred to as a lean-to roof. This is a common roof shape for rooms or storage spaces added to existing structure.
A flat roof is just that, flat. Flat roofs are easy to build and require fewer materials and labor than most other types of roofs, which is why they are so commonly used on commercial buildings. A flat roof is not very attractive on most styles of homes, but will be found on some modern style homes and many multi-family residential dwellings.