Boosting the signal here for anyone who hasn't seen these simple sets of RPG rules yet. Brendan posted a short and sweet fantasy game system with a 2d6 dice resolution mechanic, then Jack hacked it, adding more structure yet keeping it fairly light and easy.
Either one of these easy-to-run game systems would work out nicely for G+ Hangouts -- free to use, compact and easily expandable. Both iterations assume only "generic fantasy", and could easily accommodate pulp, sci-fi, historical, cyberpunk, and so on with a bit of tweaking. Both look like fun and a good start for building up something special.
I'd like to run a game over G+ hangouts at least once during the Christmas break and this 2d6 system is a strong contender. Now to decide what type of game and setting.
Update: Here's another hack of the system that lets you run games of Aliens against Predators.