From a Monty Python album, King Lear’s speech on adultery. 
I’ve always had a good memory for simple regurgitative stuff. In 3rd or 4th grade I was given the long, long Longfellow poem “Paul Revere’s Ride” to memorize and recite for a school function. I was so proud of myself for this achievement, I recited it for months afterward to any friends or family polite enough to endure listening to me.
In my single years when I’d ask a girl for her phone number, I’d say “don’t bother writing it down, I’ll remember it”. This led to a comical situation once, where I tried to call a girl and got a wrong number. Thinking maybe I had accidentally transposed a couple numbers, I tried a couple number-switch combos until I actually got her, but she seemed shocked and flustered to hear from me. It dawned on me…“ohhh-- did you switch a couple digits to intentionally give me a wrong number?” She swore she didn’t, but also said she just got out of a long relationship and didn’t want to date yet.
An incomplete list of various things I have memorized, intentinally or not, practical or otherwise:
- All relevant info for my main credit card
- Social Sec. No.
- Driver’s license No.
- Dozens of username / password combos
- Many many phone numbers, both current and defunct
- Hundreds of song lyrics
- The preamble of the Constitution (but only if I sing it, thanks to Schoolhouse Rock)
Oh yes, that Casey Jones off color poem.
How many cookies did Andrew eat? Andrew 8 8000
Phone number jingle for a furniture store that advertised heavily in a tv show I watched when I got home during grade school, roughly sixty years ago. I have never had a reason to call it.
Leaving aside song lyrics, there are a couple of random things I have memorized.
I took a Hebrew class in university and we spent an incredibly long time discussing the first two verses of the Book of Ruth. So that is one of the very few things I can say in Hebrew.
On a similar note, in a high school French class we had a fake newspaper story that we had to analyze:
Rome
“Silence, on tourne!”: un phrase tres familiere qu’on n’entend plus a studio 40 a Cinemondo. C’est la, en effet, que Guido Bravo tourne son dernier film: “Ni avec toi, ni sans toi”.
I forget the rest.
No. I mean “When in the course of human events” up through “It is their right, it is their duty, to throw off such government and to provide new guards for their future security”. It’s considered preamble because what follows are the specific misbehavior of the current king of Britain, George III.
Okay, I had never heard it referred to that way, whereas the preamble to the Constitution is one of those things lots of people used to have to memorize.
I just have the first sentence, so I’m I’m impressed you have so much more.
“The northern lights have seen queer sights. . .”
I know my wife’s SSN.
I used to know my credit card number.
I know the license plate number on my car from 1964 (41304). Comes from being pulled over so often. I also remember my first driver’s license number (181232), and for the same reason.
The resistor color code mnemonic from Navy electrician school in 1968.
“Friends, Romans, countrymen” soliloquy from “Julius Caesar”, which I had to memorize for a high school English class.
Much of the dialog in Fawlty Towers, because I’ve watched it so much, and also have the scripts in book form. 
Weirdly, as a kid I unintentionally memorized this ad - today I can still recite it word for word.
- The lyrics to a whole lot of songs
- Significant portions of the dialogue from the three original Star Wars films
- My and my wife’s SSNs
- The (landline) phone numbers from every house in which I’ve lived (including the house my family moved out of in 1975)
- A mnemonic for calculating sines, cosines, and tangents
- Significant portions of the rules for various role-playing games
A couple of things I still remember that have long since stopped being useful: my college ID number, which I haven’t needed in close to 40 years; and the combination to the lock I used on my locker all through high school.
A while back I was ripping a bunch of my old vinyl albums to mp3, and was surprised that I could still remember lyrics to songs I hadn’t heard in 20+ years.
In fourth grade, one of our teachers assigned us to memorize a poem of at least 20 lines. I chose Jabborwocky and was hooked on memorizing poems. I still remember several others from Lewis Carroll (the Mouse’s Tail, Father William, and The Walrus and the Carpenter). When I was a teenager I wrote and memorized lots of death poems–I was pretty badly depressed as a teenager–and memorized a couple dozen e.e. cummings poems, about a dozen of which I still remember. And count me in as another memorizer of “The Cremation of Sam McGee.”
The two weirdest things stuck in my memory, though:
-Once as a teenager I was walking on a dock and saw a sailboat for sale. “Huh,” I thought: The first digit is 1+3, and the first three digits are (1x300)+thirteen squared. And the fourth and fifth digits multiply to get the sixth and seventh digit." I only saw the number once and never had any reason to call it, but 469-8648 is still in my head.
-There were street preachers in my downtown who absolutely got on my last nerve. So I wrote out the Lord’s Prayer backwards and memorized it, so I could light a black candle and stalk around them, hissing it out in my meanest-sounding voice. It was totally juvenile, but then, I was a juvenile. I still mostly remember the Lord’s Prayer backwards.
It makes me feel all warm and fuzzy that so many other people also remember lyrics! If the first line of almost any song I’ve heard a few times comes to me, I can generally sing the rest.
I love his songs, but if he managed to sell all those records without a singing voice, we can certainly get by.
I’m with @Cervaise on the family birthdays; I can always remember my parents’ and brother’s birthdays, and since Mr. Legend and his mom were thoughtful enough to have birthdays very close to my parents’, I was able to remember those. My son-in-law was kind enough to be born on New Year’s Eve, so that sticks in my mind, and I just repeat my daughters’ birthdates to myself obsessively so I won’t forget them. I should set them to music.
As for useful things, I remember my credit union account number (the same since 1980), my SSN and Mr. Legend’s. I can usually fish my immediate family’s phone numbers out of my memory with a little prompting because my daughter gave me a handy mnemonic for them.
Aside from that, celebrity trivia sticks in my mind really easily, but because I let my magazine subscriptions expire 20 years ago, most of it is really out of date.
Oh, and Simpsons quotes, but I generally keep those in the family.
This reminds me: I still remember, and can recite, the Lord’s Prayer in Latin, 34 years after I had to memorize it as part of our Freshman Latin class.
Thousands of songs, without explicitly learning any, just by listening. Though for most, I need the music as a reminder. So for instance I couldn’t recite all stanzas of Dylan’s “Mr. Tambourine Man” on the spot (it’s a looong song), but I can sing along flawlessly when I play the record.
The opening soliloquy from Goethe’s Faust. It’s one of the pieces we had to learn by heart in school, and that one got stuck even after almost 40 years.
Habe nun, ach! Philosophie,
Juristerei und Medizin,
Und leider auch Theologie
Durchaus studiert, mit heißem Bemühn.
Da steh ich nun, ich armer Tor!
Und bin so klug als wie zuvor
…
In the times of digital phones, I haven’t memorized many phone numbers anymore, but still a few from close family and friends. I also remember some numbers from my childhood (my parents’ and grandparents’ and childhood friends’) that have been ingrained into my brain by manually dialing them so often.
Back when I did IT administration, I used to have memorized at least 50 passwords at a time.
Like any good Canadian, I have not memorized the lyrics to our national anthem. Usually about line three or four we starting humming and sort of lip-syncing and throwing in the odd word we can sort of remember.
I’ve found that my old driver’s license from almost forty years ago makes an excellent login PIN for my work computer. I mean, I’m never getting those neurons back anyway, might as well make the information useful.
Aside from the obvious - phone numbers, SSNs, etc - the two weirdest things stuck in my memory ate literary. In the first semester of my junior high school AP English class, we were told to memorize a passage, that we would be called upon to recite at the end of the last semester of the senior year class. Thus it is that 45 years later, I can still recite, in Middle English, the first fourteen lines of The Canterbury Tales, the prologue that begins, “Whan that Aprille, with his shoures soote…”
Then when I was required to spend two hours a day standing around at work, to pass the time I memorized the Chorus’ Prologue from Act I of Henry V (“O, for a muse of fire, that would ascend/ the brightest heaven of invention…”). I’m not word-perfect anymore - I always get tripped up by the crooked figure that can, in smallest part, attest a million - but I can still recite it with about 90% accuracy.
I still enjoy the rhythm and prosody of both passages, so periodically repeat them to myself.
On the other end of the spectrum, my sister and I can and do quote large chunks of Strange Brew to each other. " ‘Luke! I am your father! Come to the Dark Side, you knob!’ ‘He saw Jedi twenty-seven times.’ "
How about equations & formulas? The Quadratic Formula is burned in my brain. And there are certain formulas I have memorized as part of my job, such as the time domain and frequency domain equations for a capacitor and inductor, and ω = 2πf.