Unless you count some of Tolkien's shorter ones, which are really no longer than limericks, so I guess not.

I do know quite a bit of The Road to Mandalay, since you mentioned Kipling, and various other major classics like The Road Not Taken, The Charge of the Light Brigade, etc. I'm fairly sure I can still quote the first stanza of Catullus' most famous poem in Latin. But for none of those could I do the whole poem, from beginning to end.

And yeah, I guess that's peer pressure for you... kind of sad, indeed. Though it doesn't have to be that way - some of my teachers/professors in high school or college managed to make that kind of thing "cool", at least inside the walls of the classroom, so that people did appreciate it.

BG does make a good point, so your comparison to people knowing song lyrics isn't entirely apt - it's the actively trying to memorize the full text that's considered odd, as opposed to simply remembering most or all of a song's lyrics because you've heard it played dozens of times on the radio or wherever. The same might conceivably happen with a poem, but only in very specific circumstances would you be likely to hear a (longer) poem recited regularly enough to memorize it without any conscious effort.