I have found that it depends on why it broke, as to how you get it out. If you broke it by overtightening it, cutting a slot in it for a screwdriver would probably be the easiest with a dremel tool with a cut-off wheel. A screw extractor would work well too, if you can find a way to get at it. You might even take a shortened welding rod and just stick the rod to the bolt and then remove the rod from the welder's stinger, and use it as a handle.
If it broke off during removal because it's seized in the hole, IMO you only have a couple options, both of which involve removing the item that the bolt holds on. You'll have to either use a torch to heat the area that the bolt screws into and back it out with vice grips or a stud remover, or cut it off and drill it out completely. In my experience if a bolt is seized tight enough that it will round the head off, no screw extractor is going to be able to back it out.