an exceptionally clear exposition of Godel's Incompleteness Theorem, Godel's Proof by Ernest Nagel

I gave this a try. Never finished it though.

Penrose, in The Emperor's new mind does a good job of explaining the incompleteness theorem (in my opinion), though he is a bit unsound when it comes to his theory of mind (again my opinion). And Douglas Hofstader does brilliantly in Godel, Escher, Bach: An eternal golden braid, though again, some of what he says about the mind is a bit dated (yes, the field has moved on considerably in twenty or so years).