This is my master list of books that hit my sweet spot of great illustration, words I don't mind memorizing, and tried-and-tested kid appeal. It's a really short list. It's so short I published a book to put on it. If you know of more, please, for the love of llamas, tell me about them.
Behowl the Moon: An Ageless Story from Shakespeare's A Midsummer Night's Dream (Amazon | Here!): A verbatim, continuous excerpt from Puck's lines at the end of the beloved play, woven into a stand-alone story about a rambunctious crew of animals set in a vivid, slightly eerie night.
The Owl and the Pussycat (Amazon | Indiebound): Edward Lear’s nonsense rhyme is fun to recite and the detailed tropical-island illustrations on this edition, featuring views both above and below a turquoise waterline, are just as whimsical.
I carry your heart with me (Amazon | Indiebound): I was all set to make apologies for this not being a board book and then put it on the list anyway, but lo! it is being released as a board book in August! This is e.e. cummings' "[i carry your heart (i carry it in]" interpreted through some soft, lovely illustrations as a celebration of the love between mother and child.
Jabberwocky (Amazon | Indiebound): This edition has cut out the whole incident with the monster, which messes up the rhythm and sense of the poem completely. Unacceptable! but turns out I can fix that.
The Swing (Amazon | Indiebound): This simple rhyme from Robert Louis Stevenson is memorable and sweet, and the illustrations in this version are lovely. (4-2018: This is back in print!)