Gregor Lafitte's short paper: "G\"odel incompleteness revisited" is 
is a freely downloadable nice and concise overview of different kinds 
of proofs with a long list of references:

hal.archives-ouvertes.fr/docs/00/27/45/64/PDF/74-89.pdf


**Supplement of 11th October 2011:**

 In a recent paper `The Surprise Examination Paradox and the Second
Incompleteness Theorem', Notices of the AMS Volume 57, Number 11 (it
can be downloaded from http://www.ams.org/notices/201011/rtx101101454p.pdf),
the authors give a new proof for Godel’s second incompleteness
theorem, based on Kolmogorov complexity, Chaitin’s incompleteness
theorem, and an argument that resembles the surprise examination
paradox.