How are couplets used in other works of literature besides sonnets, like Shakespeare's sonnets?
Couplets--which are two lines of poetry that generally rhyme--are found in the poetry of many peoples, for example, in the Tamil poetry of India and the duilian poetry of China. In English poetry, rhyming couplets were a feature of the first English language poetry written by Geoffrey Chaucer: the famous The Canterbury Tales are written in rhyming couplets as are other Chaucerian masterpieces, like The Book of the Duchess:
I have gret wonder, be this lighte,
How that I live, for day ne nighte
I may nat slepe wel nigh noght,
I have so many an ydel thoght
REWRITTEN IN CONTEMPORARY ENGLISH
I have great wonder, by this light,
How that I live, for day nor night
I may not sleep very near to naught,
I have so many an idle thought.
Couplets are used in a number of poetic forms (poetic form: the specifications that govern different types of poetry, which may include rules about rhyme, meter, structure etc). A very popular form is the heroic couplet, which has five rhythmic divisions, called pentameter. To illustrate, Chaucer's lines above have four feet and so are in tetrameter: therefore these are not heroic couplets.
Another example is that couplets are also a feature of elegies. In English poetry, these are laments for a deceased person that mimic Roman elegies that have a complex structure and are written in rhyming couplets. John Milton wrote elegiac laments like Lycidas, which has a complex rhyme scheme that employs couplets (along with other schemes) as in this sample with three rhyming couplets (spring / string; excuse / Muse; Urn / turn):
That from beneath the seat of Jove doth spring,
Begin, and somwhat loudly sweep the string.
Hence with denial vain, and coy excuse,
So may som gentle Muse
With lucky words favour my destin'd Urn, [ 20 ]
And as he passes turn, ....