1. If you're drilling metal, use an appropriate type of bit (HSS, whatever), use some cutting lube, and drill for short periods with breaks between. Don't run the drill too fast either. If the bit overheats you'll ruin the temper and destroy the bit. Since the title of this question really should be "tell us the dumb ways you broke stuff", I'll mention that I've ruined HSS bits in maple too by drilling to fast for too long until they overheated. 

2. If you're using a drill to drive screws, most particularly those furshlugginer phillips monstrosities, use an appropriate setting on the torque clutch to prevent camming the bit out of the fastener head and damaging both the screw and the bit. Also use the torque thingy to prevent driving screws too hard into wood, sheetrock, or whatever. 

3. The back of the drill *looks* like the poll of a hatchet, but it's not a striking tool. I know, I know, why do they make it LOOK like one if it's so ridiculously fragile?! Craziness! But I learned this the hard way: You can't drive a nail with it. More subtly, you can't hammer in a screw with it either.