I've had my 360 for about 3 years now, and i've gotten the red rings probably 8-10 times with it, but I unplug the power chord in the back as soon as it happens and plug it back in, and then turn my xbox back on and its usually fine after that.
Still has happened alot though and is annoying.
Still not sure what to expect of the Mass Effect franchise, never played the first game.