Instead of drilling out a bolt that has broken off flush with or below the surface, try this:

1. Find a round punch slightly smaller than the bolt (or make one by grinding down a chisel).
2. Use a hammer and the punch to make a screwdriver-like slot on the top (broken end) of the bolt.
3. Try using a screwdriver to remove the broken bolt.

From: http://www.tradetricks.org/archives/2005_12.html