In this article, we analyze the category G-R-mod of unitary G-graded modules over object unital G-graded rings R, being G a groupoid. Here we consider the forgetful functor U:G-R-mod→R-mod and determine many properties P for which the following implications are valid for modules M in G-R-mod: M is P ⇒ U(M) is P; U(M) is P ⇒ M is P. We treat the cases when P is any of the properties: direct summand, projective, injective, free and semisimple. Moreover, graded versions of results concerning classical module theory are established, as well as some structural properties G-R-mod.