I have seen VGC'11 and VGC'12 written on smogon, and rules just posted an RMT that had VGC 2013 in it. So what exactly is VGC? It didn't take long to figure out that the number was a year, but that's all I know.
The VGCs are the Video Game Championships, yearly Pokemon tournaments. They are mainly played with doubles battles to be more fast paced. The pokemon are all limited to level 50. More info here: http://www.smogon.com/smog/issue7/vgc