The Quatrain is simply a four line stanza of any kind, rhymed, metered, or otherwise.
Like the couplet, there are many variations of the quatrain. Some of the more popular use a rhyming "abab" four line stanza alternation as below;
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.
Other variations of Quatrain include;
Envelope Stanza - the rhyme scheme is "abba", and lines 2 and 3 are enclosed between the rhymes of lines 1 and 4.
Sicilian Quatrain - iambic pentameter that rhymes "abab", from the English Sonnet genre.
Redondilla - a Spanish form written in tetrameter with any of three rhyme schemes: "abba", "abab" or "aabb".
Italian Quatrain - an envelope stanza written in iambic pentameter. Doubled (eight lines), it becomes an Italian Octave and the first half of the Italian Sonnet.
Hymnal Stanza - an alternating quatrain written in iambs. Lines 1 and 3 are iambic tetrameter, and lines 2 and 4 are iambic trimeter.
Some examples of famous poet quatrains:
From William Blake's "The Tyger"
Tyger! Tyger! burning bright
In the forests of the night,
What immortal hand or eye
Could frame thy fearful symmetry?
Omar Khayyam's "The Rubaiyat"
Here with a little bread, beneath the Bough,
A flask of wine, a book of verse—and thou,
Beside me singing in the wilderness—
Oh, wilderness were paradise enow!
The Moving finger writes; and having writ,
Moves on: nor all your Piety nor Wit
Shall lure it back to cancel half a line
Nor all your tears wash out a word of it.
Ah, make the most of what we yet may spend,
Before we too into Dust descend,
Dust into Dust, and under dust to lie,
Sans wine, Sans song, Sans singer, and—Sans End!
Why not give quatrain a go here? Come on!
Cheers!