The climate and environment where you’re building, building materials, internal shape of the building, the building’s purpose and budget will all affect the design and the shape of roof.
The followings are the most popular roof types (shapes) around the word, but the roof coverings and details are dependent to the local environment and climate.  Hip roof is the most popular roof type that almost all of us are familiar with and flat roof can be the most cost effective one in the list.