"When You are Old" by William Butler Yeats is an exquisite poem, in part because of its meaning, but also because of the sound created by its perfect rhyme scheme.
The scheme is ABBA, CDDC, EFFE. I think this pattern plays a significant role in echoing the meaning of the poem, which many say is about Maud Gunn (who Yeats' was always said to be in love with), and how he has loved her since she was young and beautiful, and loved her still as she grew old:
"How many loved your moments of glad grace,
And loved your beauty with love false and true;
but one man loved the pilgrim soul in you,
And loved the sorrows of your changing face."
What the rhyme scheme does is it changes, for example, from A to B,B, and then back to A again. By returning to the original end rhyme sound in each stanza (A, C, E), Yeats is changing the rhyme, but then returning back to each one again.
In a sense, the rhyme goes from new (young), to old, and then back to new again, sort of echoing the stages of life and how, at the end, you're able to look back on the beginning. It sort of matches this theme of reminiscing about love. He is the "one man" who loved her in this unique way because he loved her when she was both young and old, and he wants her to sit by the fire after he is gone and remember that.