The longest poem I know is Poe’s “The Raven”. I also used to know “Annabelle Lee”, but it’s slipped from my mind.
Second longest is Service’s “The Cremation of Sam McGee”. Also by Service, “My Madonna”. I’m inadvertently memorizing parts of “The Shooting of Dan McGrew”, but that one’s complicated by having the exact same meter as “Annabelle Lee” (“The moon never beams withoug bringing me dreams of the dangerous Dan McGrew…” You see the problem).
By Frost, I know “Stopping by Woods on a Snowy Evening” (made very easy by the rhyme scheme; try it), “The Road Less Travelled”, and “Fire and Ice” (but all cosmologists are required to learn that one ;)).
Like so many others, I know “Jaberwocky”, the whole thing, and can even tell you what most of the words mean. I’m quite content to be Zjestika’s and/or saramamalana’s high school boyfriend.
From Shakespeare, I know Marc Antony’s eulogy of Caesar, and Prospero’s renuciation of his powers. I keep on meaning to also learn some of Hamlet’s soliloquies and the Weird Sisters’ incantation, too, but just haven’t yet.
I can recite the Prologue of Canterbury Tales in Middle (not Old) English, up through “Then longen folks to goen on pilgrimages”. I used to know more, but I can only pull up bits and pieces after that.
From Tolkien, I can give you the “Spell of the Ring”, “Strider”, “The Road Goes Ever On”, and most of “Far Over Misty Mountains Cold”. I used to also have “Oliphaunt” memorized, but I’ve since lost the large-scale structure of it.
Emily Dickenson’s “Since I Could not Stop for Death”. I went through a phase where I was facinated by poems about death, and learned this at about the same time as I learned Poe.
Langston Hughe’s “We real cool”. I might also be able to stumble through “A Dream Deferred”, but don’t count on it.
By Ogden Nash, “Fleas” (the world’s shortest poem), “The Dog”, and “The Cow”, as well as “Purple Cow”.
Myriad Shel Silverstein poems, including but not limited to “The Walrus got Braces”, “Hug-o-War”, “Rats”, “Boa Constrictor”, “Ridiculous Rose”, and “The Fourth”. I’d love to learn “Sick”, too, but again, the lack of large-scale structure makes it very difficult.
Further in the “love to learn” department, I really ought to get a handle on some T. S. Eliott (“Wasteland”, say), and perhaps someday when I’m retired I’ll give Coleridge’s “The Rime of the Ancient Mariner” a go.