Douglas R. Hofstadter, the author of Godel, Escher, Bach: An Eternal Golden Braid edited a new edition of a wonderful 1958 book by Ernest Nagel and James R. Newman called Gödel’s Proof.
The original 1931 article by Godel is available in English translation by Martin Hirzel (On formally undecidable propositions of Principia Mathematica and related systems); I recommend reading the Nagel book first.
see also: Gödel’s Incompleteness Theorem (MathWorld), Gödel number (MathWorld)
[Photomedia Forum post by T.Neugebauer from May 22, 2007]