To keep your chain from breaking, keep the derailers properly aligned, ease off of pedaling when you shift, and don't "stomp" on the chain when it's not fully in gear. (Folks who don't go back to the non-indexed days probably never got into the habit of coasting while shifting, but it wouldn't be a bad thing to practice a bit.)
Broken chains are exceedingly rare, and are almost always the result of putting load on the chain when it's not fully in gear. The other likely source of damage is having sprockets that are so badly hooked that the chain gets sucked into a knot.