Some good points in this thread. I'd say playing with a mulligan even if you don't take it changes your score. It's like a security blanket. You can swing for the fences, take risks you wouldn't otherwise take etc... A lot of people do it though when they first start golfing. I think as soon as you start using the words handicap or score you should no longer be using the word mulligan.
It is funny though for some people it's simply too painful to have to take penalty shots off the tee. I have a buddy that will just kind of break down, mumble some crap and just kind of give up after hitting a shot (or two) OB. I've also played with people that are in complete disbelief that you have to take shot 3 from the tee box, "What do you mean!?, I've only hit one shot, *HIT* OK, that ones out too. What shot is this now?! FIVE! ARGUGH.." :)