Ok... off with my sheep's clothing now that it seems we've gotten to the bottom of the issue. I must admit, this was not a "real" concern of mine (hence the poll) but something I was interested in getting a consensus on.
I started this thread while I was working last Saturday with a friend of mine who happens to be a 30-year mechanic. He was going to put some lug nuts on and nonchalantly said, "Darn, I'm gonna have to use an extension - oh well, I'll just crank up the torque by 10 ft-lbs or so." (on the torque wrench). I started to tell him that it's not like that but it was clear he wasn't convinced so I backed off (he's a 30-year mechanic for goodness sake!)
Most of the main points were already covered by previous posts, so I'll just clarify. In addition to creating slop, extensions DO flex themselves, even with no slop in the connections. However, this flex in no way affects the torque felt by the bolt. You must expend additional energy to carry the torque through the angle, and that is why we perceive that we are applying more torque, when in fact we are simply working harder (work = torque x angle traveled). Clear as mud? Haha
Now, for the impact wrench, things are much more complicated physically. The extension is no longer relatively motionless, and the mechanism for tightening the bolt is entirely different. The extension can be modeled as a mass-spring-damper system, just like a coilover strut. When we roll over a pothole in our car, the force exerted on the wheel is of enormous magnitude and a very short duration. However, the force felt by the chasis and the driver is spread out over a much longer time, and has a much smaller magnitude. The same thing happens when you use an extension with an impact wrench.
This also sheds some light on how torque sticks work. Just as you can design a suspension to be as stiff or soft as you like, you can choose extensions that will be as stiff or soft as you like. Both affect the magnitude of the force (or torque) applied at the end.
Hope this explanation helps!