The regeneration of new plants from portions of the vegetative organs of a parent plant is called as Vegetative Reproduction.
As fusion of gametes is not involved vegetative reproduction is considered as a type of asexual reproduction.
The new plants may be produced from Roots, stems, leaves.
1. Image: http://upload.wikimedia.org/wikipedia/commons/thumb/c/c6/Stem_Cutting.jpg/220px-Stem_Cutting.jpg