Condom breakage is more likely if any of the following occur:
1) The condom is old, has been stored where it is too hot, or has been mashed up in your wallet or pocket.
2) The wrong type of lube is used.
3) You get air trapped inside the condom.
4) If the condom is the wrong size. Surprisingly, a condom may break if it is too big for the penis!
The first is obvious, so store condoms correctly, and look at the expiration dates.
The wrong lube will cause latex to deteriorate. Surprisingly, many of the lubes sold specifically for sexual purposes are not compatible with condoms. Make sure the lube says it is condom compatible, or don't use it. Also be aware of what your partner might have been playing with earlier. I've had condoms mysteriously vanish, except for the rubber ring at the base, then been told by the bottom that he had been playing with a dildo using crisco as lube before I fucked him.
Condoms are more likely to break if the rubber folds back over itself in use, and there is rubber-on-rubber friction. This is why it is important to squeeze any air out of the tip. If the tip has a big air bubble in it, and is loose and baggy, the rubber may fold up, and is likely to tear. Similarly, if the condom is too big and loose, this may happen as well. Of course, if the condom is too small, and is stretched thin, and you fuck hard, it may break, too. But, I've seen guys with small dicks have condoms break, more often than I have had trouble (I'm about wrist-thick and pound hard) and it seems to be because the condom is too loose, and gets wrinkled up.