I have broken a stud, and my local tire store had a replacement stud- you can use a punch to drive the broken stud out, and then you use the tools you have to seat the new stud in place (a fun little project, all in all). Also, I have screwed up an alloy wheel when I didn't re-torque it, as Toby advised. It's important to have the correct lug nuts for your wheel as well- steel wheel lugs aren't supposed to be used on alloy wheels (don't ask me how I know that please).
I have also seen cracked lug nuts- inspect them carefully, they might be older than you are...