In at least two different contexts now (installing shower handrails, installing gate on fence) I've found myself stripping the head of the screw beyond all use. I must be doing something wrong, so what is it?
The screws I'm driving are two or three inches long with a Phillips head. I'm using a cordless drill with a Phillips bit. I find that no matter how hard I push from behind the drill (even with all the body weight I can muster) and no matter what speed I drive at, the drill bit jumps out of the head of the screw. When that happens repeatedly (either because I think I can make it if I just push it harder, or I get frustrated), the head ends up getting stripped and then I've got multiple problems (getting the screw out, replacing it, and getting the replacement in without stripping it) that set the project back. What am I doing wrong?
UPDATE: Thanks to all who contributed to the great answers below! After checking my screws and bits (Phillips, not Pozidriv; right size, not worn), drilling wider pilot holes and then being careful with the speed and torque, I decided I wasn't using the right tool for the job (what's that they say about bad workmen?) and I went and got an impact driver. Then the first few screws went in like magic --- it was incredible! And then it sheared off the heads of the next couple of screws. Grrr! I couldn't manage to get the remnants out, and ended up drilling new holes in which I tried some new store-bought screws --- same result. Double grrr! So I drilled some new holes and tried some hex-head screws, which went in just fine with a socket on my cordless drill. Hurray!
Conclusion: I hate Phillips heads for high-torque situations; I much prefer hex heads. That's how I settled this particular matter, but there are some very important and useful answers below that were not "accepted" that nevertheless may help people in slightly different circumstances.