Vegetative reproduction is asexual reproduction, but other terms that apply are vegetative propagation and vegetative multiplication. In essence it is those processes by which new plant "individuals" arise or are obtained without production of seeds or spores. It is both a natural process in many, many plant species and one utilized or encouraged by horticulturists to obtain quantities of economically valuable plants.
Natural vegetative reproduction is mostly a process of herbaceous and woody perennials, and typically involves structural modifications of the stem, although any horizontal, underground part of a plant (whether stem or a root) can contribute to vegetative reproduction of a plant. Most plant species that survive and significantly expand by vegetative reproduction would be perennial almost by definition, since specialized organs of vegetative reproduction, like seeds of annuals, serve to survive harsh winter conditions.
A rhizome is a modified stem serving as an organ of vegetative reproduction. Prostrate aerial stems, called runners or stolons are important vegetative reproduction organs in some species, such a strawberry, numerous grasses, and some ferns. Adventitious buds develop into above ground stems and leaves, forming on roots near the ground surface and on damaged stems (as on the stumps of cut trees). Adventitious roots form on stems where the latter touch the soil surface.
Man-made methods of vegetative reproduction are usually enhancements of natural processes, but range from simple cloning such as rooting of cuttings to artificial propagation by laboratory tissue cloning. Fruit tree propagation is frequently by budding or grafting, which preserves clones of desirable varieties.