It would depend on the game. Something like CoD4, where you join some random group and fight doesn't usually require a mic. No one is going to coordinate their attacks, they just want to kill the enemy. If I play with friends, we just make our own XBL party and talk in there.
But a game like L4D where teamwork is a key aspect to winning, without a mic to communicate plans, give warning, and call for help, you become a liability. I usually play with friends on L4D, and we have a strict rule on having a mic. We'll even kick people from the lobby if they don't have a mic and will be on the other team, because we want the other team to be challenging, too. If someone that has a mic doesn't even use it or allows themselves to be beaten up by not calling for help, they are out.