Quatrains are four line stanzas of any kind, rhymed, metered, or otherwise. Like the couplet, there are many variations of the quatrain. Some of the more popular as passed through tradition are:
Alternating Quatrain- a four line stanza rhyming "abab." From W.H. Auden's "Leap Before You Look"
The sense of danger must not disappear:
The way is certainly both short and steep,
However gradual it looks from here;
Look if you like, but you will have to leap.
Envelope Stanza- a quatrain with the rhyme scheme "abba", such that lines 2 and 3 are enclosed between the rhymes of lines 1 and 4. Two of these stanzas make up the Italian Octave used in the Italian sonnet. This is from Auden's "Look Before You Leap"
The worried efforts of the busy heap,
The dirt, the imprecision, and the beer
Produce a few smart wisecracks every year;
Laugh if you can, but you will have to leap