My 8 and 11-year old daughter and I all memorized Longfellow’s Paul Rever’s Ride this year.
Long poems I memorized in my youth:
How The Grinch Stole Christmas by Dr. Seuss;
The Jabberwock,
The Walrus and The Carpenter,
You Are Old, Father William, and
Large sections of The Hunting of the Snark, all by Lewis Carroll;
Kubla Khan by Samuel Taylor Coleridge;
The Pied Piper of Hamlin by Robert Browning;
The Perfect High or The Quest of Gimmesome Roy by Shel Silverstein.
The last is the only one I remember in its entirety, which I find vastly amusing because I memorized it one night while high on acid. Bizarre, huh?
e. e. cumming’s she being Brand
It just speaks to me, ya’ know. In a language that’s fairly perverted and forever stuck in the gutter, but speaks nonetheless. 
And just because they cracked my stuff up, both Christopher Marlowe’s The Passionate Shepherd to His Love and the tongue-in-cheek retort of Sir Walter Raleigh’s The Nymph’s Reply to the Shepherd.
*And on the pedestal these words appear:
My name is Ozymandias, king of kings:
Look on my works, ye Mighty, and despair! *
I had to memorizeit for 10th grade history. My teacher swore once we learned it, we would never forget it. It took me an hour and a half to remember the name. I think she was mistaken.
Like several here before me: “The Cremation of Sam McGee,” because I had to in about the eighth grade or so. I have almost completely forgotten it.
And also like several here before me: “Jabberwocky,” but just because I wanted to, 35 years ago. If I strain my brain, I can still recite it.
I had to memorize about half of The Mermaid by Alfred, Lord Tennyson in fourth grade (hated it!!).
I also had to memorize Kubla Khan by Samuel Taylor Coleridge in eighth grade. (That one was slightly better; we got a big kick out of calling him “Samuel Taylor Coleslaw”.)
She lived in storm and strife
Her soul had such desire
For what proud death may bring
That it could not endure
The common good of life
But lived as 'twere a king
That packed his marriage day
With banneret and pennon,
Trumpet and kettledrum,
And the outrageous cannon.
To bundle time away
That the night come.
Yeats got me through some tough times. I used to remember several more but they’ve faded. Things fall apart you know.