On behalf of other Bambis – we don’t all strip screws, TYVM. 
I must have missed the part of any of his posts where he said he thought he had done something to improve the situation.
If I may…
If you are installing something that has pretty finish (usually brass) screws, the heads are really easy to strip because the metal is much softer. So, before you do the project, take the brass screws down to your local hardware store and get a 2-3 steel screws of the same size.
Use the steel screws first, to tap the hole. Then remove the steel screw and replace it with a brass screw.
Not a bad idea! 
I mean, really, if it’s not something like the finish having to match for cabinet hinges or if the screws are hidden or whatever, this is a good idea even for permanent use.
I generally drill a small pilot hole fisrt. But, I’ve found that using the using right size driver bit (whether phillips, torx, or square) is the most important thing. Well, that and paying attention.
One other thing to note, doing it by hand doesn’t guarantee that you won’t strip heads, in case anyone’s wondering. Using the wrong size tool and then really bearing down can round out the screw head just as bad as a careless power tool user.
Now, this is my pet peeve - square head screws are called “Robertson” screws, after the Canadian that invented them.
Now you can impress all your buddies with your new-found knowledge! 
(And that is a great idea, GrizzRich.)
I have the cute little three bit case.
http://www.sears.com/sr/javasr/product.do?BV_UseBVCookie=Yes&vertical=TOOL&pid=00952154000
But I had it for 3 years, and never used it. I know how to use my Torque settings and I have sharp screw bits that don’t slip. So I never have stripped screws.
I’ll bet this is due to the same phenomena due to which:
It doesn’t rain after I’ve RainExed, or doesn’t snow when I’ve bought a nifty new shovel, or any of those other things where, as soon as you prepare for them, they don’t happen.
In the interest of science(and to deal with my boredom) I ran the following experiment.
Supplies:
1 3.5 inch brass phillips head deck screw #8 diameter
- 2x6 of indeterminate hardwood
- 2x4 of pine
- 18 volt corldless drill/driver with standard accompanying phillips bit.
- Dremel with #953 Alum. Ox. Grinding Stone (http://www.dremel.com/html/home_fr.html)
1 no.1 craftsman screw-out
Methodology.
I stacked the 2x6 on top of the 2x4. I then used the phillips bit to screw the deck screw into the stack, with no pilot hole. I changed to highest torque and let it screw as far as it would go. The screw was sunk about 3/16 of an inch below surface. I then took Dremel to grind away screw top until it was a cone shaped hole with no noticable features. I believe it represented the most stripped a screw can get. I put the no.1 screw-out in the drill and put it on reverse. Using the slowest speed possible, I attempted to remove the screw. Using the entire weight of my upper body there was still significant slippage, but the screw was extracted.
Verdict:
It does work on brass even in the most severly stripped cases.
Other concerns:
The no.1 screw-out bit is noticeably less sharp than it was before. The slipping dulled the bit significantly, such that I doubt I could get more than three or four out before the bit is useless. In the future I believe it will be better to use a hand-driver than the electric drill to control slippage of the bit.(Thank god for Craftsmen free replacement)
Have I ever mentioned what an awesome message board we have here?
Sears could pay you commission! I’m adding the screw-out to my list of “need to haves”.