I think I am at a slight advantage here.

I know the beginning of Puck's speech from the end of Midsummer Night's - one of my favorite of Shakespeare's...

  If we spirits have offended
  think but this and all is mended
  that you have but slumbered here
  while these visions did appear...

and then the end, yes?

  all that we see and seem
  is but a dream within a dream

For a while I had the beginning of Romeo and Juliet memorized - the intro. If I heard it I could probably speak with it but alas, I cannot conjure it out of the ether.

And from Romeo and Juliet; "Ah! That's a degree to love!" R&J are talking and J says she pities R and he says that then. It is a line that makes me think.

I will go you neck-to-neck on Simon & Garfunkel, too :) - I have squandered my resistance on a pocket full of mumbles such are promises. (Their "Cecelia" is my formative song.) I could do a lot of song lyrics. Billy Joel. Build Me Up Buttercup.

And countless poems, which I think has come up in discussion on Hubski somewhere before. I've memorized: The Raven - though some of it I've lost - the first poem I ever memorized, and this is my inner geek coming out, was The Lay of Luthien from LOTR -

  The leaves were long, the grass was green
  the hemlock-umbels tall and fair
  and in the glade a light was seen
  of stars in shadow shimmering
  Tinuviel was dancing there
  the light of stars was in her hair
  and in her raiment, glimmering. 

  There Beren came from mountains cold
  and lost he wandered under leaves
  and where the Elven river rolled
  he walked alone, and sorrowing... 

Oh, la, lord of the rings, be still my heart. I recited that in front of my eighth grade class and then gave them a lecture on iambic tetrameter and rhyme scheme. Woooo I was popular ;)

I have Dickinson memorized (Hope is the thing with feathers...), I have Frost (Whose woods these are I do not know). I've memorized Philip Larkin's This Be The Verse and Atwood's "You Fit Into Me," Muriel Rukeyster's "the Conjugation of the Paramecium," like thenewgreen I have memorized Bishop but I went for "The Art of Losing." Wordsworth's "The World Is Too Much WIth Us" and Neruda's "Love."

Interestingly, I do not have any poems of mine memorized.