Alright then.
It's round like an apple, and deep like a cup,
yet all the king's horses can't pick it up.
All of Humpty Dumpty's pieces?
Since it describes the object as being "round", like an apple, which isn't perfectly round OR oval, and deep like a cup, well it must be something with a small, yet hollow inside, when he falls off the wall, he cracks apart, causing all of his contents to run out, meaning he's empty like a cup.
And then the "yet all the king's horses can't pick it up.", is a reference to the line "all the kings horses and all the kings men, couldn't put him back together again", but to save space, and for it to "riddle" like, they removed the "kings men", so the answer wasn't given away; and also they can't pick up all of his pieces, because if they did, they'd be able to put him back together again.
EDIT: Now that I think about it, it's probably a
SADDLE.