In 2006, GN'R used the long Jaws like theme, which is widely believed to be The General, they used this all throughout 2006 and 2007 to my knowledge. Then in 2009 (Asia), and early 2010 (Canada), they started to mix it up abit and started to use other intros. Some include the Dexter theme, Everybody Knows by Leonard Cohen and another one which is an old American crime sitcom, maybe someone can name it?..... anyway they started to use all of these as well as the original intro from 2006 "The General".
During the 2010 European tour, they started to use another Jaws like theme, which is again believed to be The General but from a different point in the song. I believe they used this as well during the late 2011 / early 2012 US shows. Then since the 2012 European tour, they have been using Massive Attacks - Splitting The Atom, which works GREAT live.
That's about right I think...