There are many Ecclesiastical Latin hymns that incorporate a rhyming scheme that sounds very satisfying to an English ear. One common example:
Tantum ergo sacramentum
et antiquum documentum
novo cedat ritui
praestet fides supplementum
It struck me, though, that I have never encountered a tail-rhyme scheme in any classical poetry I have seen. It all appears to be written in "blank verse" (to continue the comparison with English) with varying meters, especially dactylic hexameter.
Are there any classical examples of poetry with a rhyme scheme? Obviously, rhyme existed at this time, but I am looking for examples where it is more than a one-off flourish--as, for instance, alliteration and assonance might be considered.
If there are not any examples, I would also be interested in knowing when this started and why.