Stolon
A stolon is an aerial shoot from a plant with the ability to produce adventitious roots and new offshoots of the same plant. The complex formed by a mother plant and all it's offshoot connected by stolons are considered to form a single individual. A stolon is a propagation strategy akin to a rhizome.
Note that some species of crawling plants can also sprout adventitious roots, but these are not considered stoloniferous: a stolon is sprouted from an existing stem.
Examples of plants that extend through stolons include some species from the Fragaria, Hieracium genera, Silverweed and Bermuda Grass.