Rhyming in poetry can can add depth and feeling, as in Yeats:
"WHEN you are old and grey and full of sleep,
And nodding by the fire, take down this book,
And slowly read, and dream of the soft look
Your eyes had once, and of their shadows deep;"
Loosely translated from an older poem by Pierre de Ronsard, btw, with the same rhyme scheme.
"Quand vous serez bien vieille, au soir, à la chandelle,
Assise auprès du feu, dévidant et filant,
Direz, chantant mes vers, en vous émerveillant :
Ronsard me célébrait du temps que j’étais belle."
Or, Brownings Last Duchess, a narrative poem of rhyming couplets, so skillfully done that we hardly notice them.
That's my last Duchess painted on the wall,
Looking as if she were alive. I call
That piece a wonder, now: Fra Pandolf's hands
Worked busily a day, and there she stands.
Or Wilfred Owen:
Men marched asleep. Many had lost their boots
But limped on, blood-shod. All went lame; all blind;
Drunk with fatigue; deaf even to the hoots
Of disappointed shells that dropped behind.
Or Rupert Brooke:
White plates and cups, clean-gleaming,
Ringed with blue lines; and feathery, faery dust;
Wet roofs, beneath the lamp-light; the strong crust
Of friendly bread; and many-tasting food; 30
Rainbows; and the blue bitter smoke of wood;
And radiant raindrops couching in cool flowers;
And flowers themselves, that sway through sunny hours. . .
The rhymes never intrude upon the narrative; they're almost invisible unless you concentrate on them
Then we have Eliot. No rhymes -- but rhythm, and evocative in the extreme:
APRIL is the cruellest month, breeding
Lilacs out of the dead land, mixing
Memory and desire, stirring
Dull roots with spring rain.
Rhyme in poetry is just one tool, like metaphor, meter, imagery, etc. To rhyme or not is a choice, appropriate to what you are writing. Rhyme, or lack of it, has little to do with the essence of poetry. It can add or detract -- depending on the skill of the poet.