Traditionally, Western couplets are smart rhyme, although not all couplets rhyme (a poem may use white space to mark out couplets as well). Couplets with a meter of iambic pentameter are called heroic couplets. The Poetic epigram is also in the couplet form. Couplets can also play a role in more complex rhyme schemes. For example, Shakespearean sonnets end with a couplet.
Rhyming couplets are one of the simplest rhyme schemes in poetry. Chaucer's The Canterbury Tales are written in rhyming couplets. John Dryden in the 17th century and Alexander Pope in the 18th century were both well known for their writing in heroic couplets.
Because the rhyme comes so quickly in rhyming couplets, it tends to call attention to itself. Good rhyming couplets tend to "snap" as both the rhyme and the idea come to a quick close in two lines. Here are some examples of rhyming couplets where the sense as well as the sound "rhymes":
On the other hand, because rhyming couplets have such a predictable rhyme scheme, they can feel artificial and plodding. Here is a Pope parody of the predictable rhymes of his era: