Texts I have memorized over the years:

Shakespeare sonnets. Probably 60-70 of them. I can only recite about half that number now. A few soliloquies from Hamlet. Prologues from Henry V.
Beckett's Ill Seen Ill Said. A good chunk of this text. The most prose I've ever memorized. I can't recite any of it know. Beckett's "Ohio Impromptu." A short play with only one speaking part.
Claudio Rodríguez. Probably 40-50 poems. I can relearn these quickly whenever I want.
WCW: Most of the famous shorter poems, and a few known only to a few readers. I can relearn these easily whenever I want as well. Some I've never forgotten.
Frost: Most of the better known sonnets and a few other short poems.
O'Hara: Two or three of my favarites like "To the Harbormaster."
Yeats: Maybe a dozen poems.
Keats: Some of the Odes. I have to relearn them each time.
Stevens: Quite a bit. Mostly shorter poems. I memorize them quickly but forget them again.
One or two poems a piece by numerous others, Creeley, Bécquer... a lot of anthology poems, "Go, lovely rose..." "Rose cheeked Laura, come."

Memorability is a funny thing. For example, Barbara Guest is one of my favorite poets, but I can't seem to memorize her poetry with any ease. She doesn't have that particular kind of "stickiness." With cummings I retain the rhythm but don't remember the particular words: my father moved through dooms of love / through blanks of blank, through blanks of blank / singing each morning out of each night / my father moved through blanks of blanks." My 99-year old Grandmother has plenty of texts by memory, so maybe it's genetic. Some people memorize, some don't. I can't say we memorizers are superior, but I can't imagine not doing it. I can do it quickly, but don't retain all that well...