One example is terza rima, which is written in tercets with a rhyming pattern ABA BCB CDC.
Robert Frost made use of Rubaiyat in chain rhyme form in his poem, "Stopping by Woods on a Snowy Evening."
It helps the poet to shape the poem and the reader to understand it; creating a link between sound and thought.
Two examples of chained verse from William T. Dobson Poetical ingenuities and eccentricities, London, 1882 (see text here for the sources of these examples) Truth Nerve thy soul with doctrines noble, Noble in the walks of time, Time that leads to an eternal, An eternal life sublime.
For instance, the popular French song Trois petits chats consists of chain verse.