Nothing game specific.
A little bit of information on the group:
We set up LANs for Console and PC games
We are a school group, so nothing violent/gory
We do Xbox 360, PS3, Wii, and PC LANs
It's all about having fun and celebrating the fact that Gaming can bring people together in a positive way.
A good example of a logo is the MLG logo:

Simple, is easy to identify as a gaming organization, and is iconic.