I have broken several impact pullers, but still keep one around for occasional use. Aside from the fact that they don't work very well for pulling light bullets, they can also loosen the cores in non-bonded jacketed bullets--not so much you'd notice, but enough to make them shoot really weird.
I use an RCBS collet puller for smaller caliber bullets, but use the side-cutter method describer earlier for larger bullets, especially those with cannelures. It's amazingly effective and if done with the least possible pressure doesn't affect accuracy at all.
