I think everyone has heard the phrase "rhyme or reason."
The phrase is recorded in English as far back as the 15th Century--in a rhymed couplet--
As for ryme or reson, ye forewryter was not to blame,
For as he founde hit afore hym, so wrote he ye same.
The evident distinction between rhyme, standing for poetry, and reason, standing for rational definition--goes therefore as far back to a time when our sense of the meaning of poetry included the concept of rhyme as in sound. Rhyme and poetry were synonymous, or at least ineluctably linked. The attraction of like sounds to like, in measured lines, was deemed obvious--the same quality of inevitability we've noted before in the history of aesthetics, as a description of a practice as if a development were natural and predictable.
Rhyme is noted as far back as the 10th Century BC, in China, and was employed by the ancient Greeks. The Irish seem to have adopted rhyme as a method of poetic composition as early as the 7th Century. The actual origins of rhyming are clouded in antiquity, so it is highly unlikely we will ever really know how rhyme was invented, or who did it. Of greater moment in my discussion, however, is the enthusiasm with which it was adopted throughout Europe during the Middle Ages, and after.
In Milton's Preface to Paradise Lost , he says this:
The Measure is English Heroic Verse without Rime, as that of Homer in Greek, and of Virgil in Latin; Rime being no necessary Adjunct or true Ornament of Poem or good Verse, in longer Works especially, but the Invention of a barbarous Age, to set off wretched matter and lame Meeter; grac't indeed since by the use of some famous modern Poets, carried away by Custom...
He seems indeed to be repudiating his earlier genius in rhymed verse, at least as applied to the writing of an Heroic Epic, such as Paradise Lost. Much of the greatest English poetry is written in blank verse--Shakespeare's plays, Wordsworth, Shelley, Keats, Tennyson. Milton calls rhyme a "barbaric invention" written by poets "carried away by Custom...." Harsh words.
Rhyme in longer sequences of narrative has a monotonous, even annoying effect. Certainly by the latter half of the 19th Century, poets had had enough experience of rhyme--600 years of it!--to view it with a certain ambiguity. I have written earlier here about Arnold and Hopkins--whose use of rhyme has a plodding, earthy quality. Poe, like many of his Victorian Age contemporaries, seems to have thought of rhyme as a dreary tolling, signifying morbid senescence and death. That's true of much of Tennyson's work as well.
We think of decadence as the decaying of inspiration over time, it also signifies a fullness or over-indulgence, the ulterior ripening of a life-form. Certainly, over the arc of time in which rhyme was used in English poetry, there was a kind of slow reckoning with respect to the qualities of the pure English lyric. In Donne's hands, for instance, the lyric poem becomes like a metaphysical lecture (or sermon) with the finest conceits and figures of wit. And yet, even with him, there is a heaviness, as of a truncheon-blow, in the end-rhymes. So much gloom inhabits the English rhymed lyric between Chaucer and Browning. Think of Keats's Odes.
One way to consider rhyme--and its inherent quality--is to think of it in terms of opacity or translucence. Are two words that share a common (syllabic) sound a "see-through" in which their respective separate meanings are "visible" through each other? Or, conversely, are two words which rhyme a kind of "dead-end" in which the coincident separate meanings are "stopped" or made blank? Equivalencies tend to reflect or "mirror" meanings back upon themselves--which is how I believe rhyme usually functions in verse. Rhyme-schemes set up predictable expectations which are then confirmed (realized) or not. Variability may be defined as the avoidance of repetition. Unnecessary versus necessary repetition.
A definition of rhyme is of an arbitrary necessity imposed on the meaningful variability of language. Since almost all sound qualities of words are arbitrary assignments, the limited subset of possible rhyming words (or phrases) is a severe narrowing of the possible formations of meaning in language. The challenge of overcoming this inherent limitation makes of rhymed verse a minor diversion from the rich potential of linguistic variability. One could make a case for "internal" rhymes--that is, rhymes which occur across the fabric of lines, whether set or not--being a more natural expression of the common qualities of sound--but self-consciously hard rhymes, even "mixed" in, tend to over-dominate any sequence in which they occur. This over-emphasis tends to push the argument of any poem in which it's employed into heavy irony, pretentious humor, or patronizing condescension. In the age of Dryden, these kinds of poses may have seemed apposite, but today they sound merely hoary and antidiluvian.