It's rather startling to read contemporary poetry that rhymes. And Pity the Beautiful: Poems by Dana Gioia is startling in exactly that way, and more.
There's a name for this, of course; we have to give everything a name: The "New Formalism." It reaches back to a time when most poetry did indeed rhyme, and was metrical as well. It was also a time (roughly pre-World War II, perhaps a little earlier) when poetry has a much broader appeal than it does today. Newspapers, for example often published poetry on a daily basis. The poets associated with the New Formalism include Mark Jarman, Howard Nemerov, Donald Justice, Mary Oliver - and Dana Gioia.
Even after World War II, rhyming poetry was still taught to schoolchildren. I can remember learning (and doing a class-in-unison recital) of Longfellow's "Paul Revere's Ride" in the fifth grade. It was nationalism and poetry and performance art in one nice package.
And that is partially the point Gioia makes in Can Poetry Matter?, his collection of essays about poetry and American culture, that the post-war shift of poetry largely to academia essentially shut the door on poetry for the public. Poetic forms and techniques like rhyme (and meter) were largely abandoned.
Gioia has been working to resurrect both more traditional poetry and "Poetry for the public," and Pity the Beautiful is more than a nod in that direction.
The important point about rhyme is that it's memorable and accessible, and it makes recall easier. Consider the opening lines of Gioia's poem "The Reunion:"
This is my past where no one knows me,
These are my friends whom I can't name--
Here in a field where no one chose me,
The faces older, the voices the same.
It's not only rhyme that's at work here; meter and cadence are strong elements as well. Say the lines aloud - they're written to be read aloud.
Not all of the poems in the collection are "new formalist," but they share elements of similarity, particularly in how they flow in an orderly, formal way.
The poems are also distinguished by their subjects, like freeways, shopping, a children's hospital (a poem that is particularly moving), an apple orchard, a coat. These are subjects and themes that are familiar, recognizable, without abstraction. And each has a kind of narrative flow. One poem, "Haunted," is a story of what might be love found and lost.
What differentiates these poems from older poems like Longfellow's is the language - it's contemporary. Gioia avoids ornate or complex words; instead, he aims for the simple, often paired them in rhyme, and their simplicity is the power of each poem.