JRR Tolkien's “Lord of the Rings” is filled with poetry of his own composition. While this poetry is not really a significant contribution to the Western poetic canon in the same way the novel is to the genre of fantasy literature, it is probably more widely-read than just about all of the famous poetry of the twentieth century just by virtue of being part of such a popular novel.
Tolkien's poetic achievement probably deserves more recognition than it generally gets. There are several reasons for the neglect. One is that all of these poems are set squarely in the fantasy context of Middle Earth, so they can't easily be read or appreciated beyond that context. Then there's the fact that twentieth century poetry has almost completely rejected formal technique, but Tolkien went in exactly the opposite direction. His poems are technically expert exercises in various ancient forms of verse, some of which are highly demanding. The main reason his poetry is not read for its own sake is probably this anachronistic quality.
He liked to write in the accentual meter of “Beowulf” and the other Old English epics such as “Sir Gawain and the Green Night.” He also wrote in the ballad form. One of his longer pieces seems to be in conscious imitation of the Welsh bardic forms known as “cynghanedd.” The fact that he largely succeeded in imitating this incredibly complex form in English would be widely seen as an impressive technical feat, if impressive technical feats still carried any weight in modern English-language poetry!