InGaN alloys with (0001) or (000) polarities are grown by plasma-assisted molecular beam epitaxy. Scanning tunneling microscopy images, interpreted using first-principles theoretical calculations, show that there is strong indium surface segregation on InGaN for both (0001) and (000) polarities. Evidence for the existence and stability of a structure containing two adlayers of indium on the In-rich InGaN(0001) surface is presented. The dependence on growth temperature and group III/V ratio of indium incorporation in InGaN is reported, and a model based on indium surface segregation is proposed to explain the observations.