Lots of poems fit that description. One of my favorite though is "Annabel Lee" by Edgar Allen Poe. The poem is linked below.
Poetry repetition is going to repeat a word or phrase in order to emphasize its significance and call special attention to it. In the poem "Annabel Lee," the name Annabel Lee is repeated frequently throughout the poem. The other lined repetition is the line "In this kingdom by the sea."
"Annabel Lee" does have poetic rhyming to it. It is not couplets or even the common "abab" rhyme scheme. The first stanza's rhyme scheme is ababcb. 2nd stanza is "dbebfb." As you can see in that stanza, only the rhyming of "sea" words is being done. Poe does finish the poem with two back to back couplets, which is a stark enough departure from the rest of the poem that it really stands out.
Alliteration can be found at various points of the poem, but the final two lines make heavy use of the "s" sound.
"Here the loud alarum bells-
serves for the alliteration.