According the the Wikipedia page, the second generation proof is up to at least nine volumes: six by Gorenstein, Lyons and Solomon dated 1994-2005, two covering the quasithin business by Aschbacher and Smith in 2004, and one by Aschbacher, Lyons, Smith and Solomon in 2011. However, this latter book is really just the second part of an outline of the proof, the first part of which was written by Gorenstein in the 80s (the reason for the delay is, of course, that the quasithin case hadn't actually been settled at the time of the announcement of completion). Hence the last update on the second-generation proof is really 2005.
With the recent formal proof in Coq of the Odd-order Theorem, it would be good to know where the traditional proof is up to.
EDIT 6 August 2013: Any news as to the completion of that seventh volume as mentioned in the comments?
EDIT 29 September 2016 Just a bump to this question in case people know more about where the progress is at. Books 7 and 8 should probably have made some progress since I asked this originally.
Best Answer
There is an interesting review by Ron Solomon of a paper in this area, which has been featured on the Beyond Reviews blog. In particular, he outlines the broad tactics that people are using in CFSG II, and some of the content that will be going into volume 7.
Also, Inna Capdeboscq apparently gave an outline of volume 8, or at least a chunk of it, at the Asymptotic Group Theory conference in Budapest. This was mentioned by Peter Cameron on his blog, sadly with no detail! If anyone can get a whiff of what she said, I would be grateful.
EDIT 15 October 2016 I emailed the group-pub mailing list and was told second-hand that Ron Solomon 'has hopes' volume 7 will be submitted next year.
EDIT 27 March 2018 Thanks to Timothy Chow in a comment on another answer, here is the link to the published version of Volume 7. So now the countdown to Volume 8 starts...
EDIT 22 June 2018 Even better news: Volume 8
Also (from the same article):
EDIT Mar 2019 Volume 8 has been published. The page listing the available volumes, along with links to more details is here.
The summary of this volume is as follows:
EDIT February 2021 Volume 9 has now been published. From the preface:
EDIT September 2021
In response to a question from Hugo de Garis, Ron Solomon sent the following email in January 2021:
(Emphasis added)
EDIT 29 Dec 2021
Richard Lyons maintains an erratum for the whole published second generation CFSG on this page: https://sites.math.rutgers.edu/~lyons/cfsg/
EDIT 05 Apr 2022
In response to a further question from de Garis (see the page linked above), Solomon wrote (in March 2022):