I As far as I know what breaks them is either fingernails or insuficient lubrication.
Oil-based lubricant (like vaseline or baby oil) can cause breakage as well. Check the packaging of any lube you use to make sure it's condom safe, and don't use stuff as lube that wasn't sold to be used that way. They can also break if they are too tight, or if they're expired. Yes, condoms do expire... they all have expiration dates printed on them. If it gets close to or past that date, the latex has most likely weakened and you'll want to toss it.
Another good thing to do is make sure you pinch about 1/2 inch of the tip of the condom before you roll it on, so there's enough airless space for the ejaculate to go. If there's no extra space when you come, it could easily break through.
You also want to be very careful when opening them, keep them out of extreme heat or cold, and avoid storing them in places where they'll be susceptable to a lot of friction (like your wallet in your back pocket all day long).