"Am I using a bit that's too small? Too large? Am I not pressing hard enough? Are my pilot holes too small? (The last is a distinct possibility.)"

All or any of these could be contributing. There are several sizes of both phillips and flat screwdriver bits, and only one that really fits any given screw correctly. Also, many cheaper driver bits are soft and wear out very quickly. You could also be failing to hold the axis of the driver in line with the axis of the screw.

Practice a bit:

Make sure the pilot hole is about the same size as the inside diameter of the screw threads, especially in hardwoods.

Make sure the bit fits the screw really well and is in good condition.

Don't rely on just your hand and forearm strength to hold the bit in the screw - get your face close to the part you're working on and position your body so you can throw some weight into it.

Make sure the driver is in line with the screw.

Take your time. With an electric driver, use that variable speed to start slowly; don't just grab the trigger as if you were yanking the tablecloth out from under some expensive crystal.

You'll get there.

Cheap screwdrivers are probably the number one cause of problems with Philips type screws.
The tip must be correctly ground to shape, size, and hardened. Miss any one and it ruins the screws in short order.
#1 Philips is probably the most common size, so spend a few extra dollars on a good screwdriver.

The same thing happens with hex recess screws that need an 'Allan' (hex) wrench. Cheap wrenches are poorly sized and rarely hardened correctly.
If a free wrench comes in something throw it out and use your own.
Bondhus and Allen both make good sets for less than $10.

More donuts. You just need to bulk up some, thats all. Join a gym, and spend some time in the weight room. Everybody strips out screws, even those of us who could stand to lose a few pounds. But mass, with some of it muscle, does help. I have a rather heavy Milwaukee drill, with an anti-torque handle that screws in to the body, so I can hang on with both hands if needed. With a fresh philips bit in the chuck, that would be my tool of choice if I was asked to assemble a bed frame. This tool is overkill for driving screws, but it works great for this purpose. No batteries, it runs off the nearest outlet. It has a variable speed control, as well.

Thanks for the advice, everyone. I especially like the donut suggestion. :-)

I've always put some thought into matching bit to screw, but clearly my decisions have not been the best. I mostly use a Black & Decker screwdriver set with a multitude of bits. The Philips bits are so pointed...I end up drilling the screws instead of turning them.

I have an old electric Craftsman drill, and I often borrow my son's big B&D cordless drill. I also have a rechargeable B&D screwdriver. So I have a wide choice of bits. I'll pay more attention to proper fit.

By the way, a couple of years ago I assembled an armoire without any power tools. It was an aerobic activity.

The #1 bit has a point a #2 and larger will have a flat point to seat in the screw recess better, a phillips is made to cam out to prevent breaking the head off.

Just wanted to let you know the bed assembly was a snap! Only six screws, and they don't hold anything really major together. The bed looks great. I then went on to install three mini-blinds and three wooden curtain rods. No stripped screws there either...but I did break one drill bit. :-)

Thanks again!

Susan

In addition to the above:
- Buy good quality screws that are harder than the corner hardware store DIY-handyman variety. You may need to go to a specialty woodworking store or mail order source. McFeeley's, Red-Top Screws and Stuff, Rockler and Woodcraft all have them.
- Stay away from drywall screws unless you are installing drywall
- Lube the screw threads with a little wax (paraffin, candle, or beeswax) or vaseline
- Switch to Robertson (square) drive screws. Phillips were actually originally designed to cam out so they couldn't be overtightened.
- Use a clutch setting on your cordless driver

What is the screw material?
You did not mention if you are driving brass or steel screws.
Brass screws should not be driven into new holes. Drive in teh same size screw in steel till barely snug, back it out, then us e a brass screw.
Using a brace instead of a power driver will also help with harder driving jobs.
Incorrect hole sizes will also break screws (or strip) very quickly.
For softwoods you can dril slightly smaller than thread root diameter, but for hardwoods you need to be very close to root diameter to prevent problems.
Power drivers are generally a bad idea on finished projects.