What can you do with a broken tap? Make a center punch!
Originally uploaded by nickjohnson
A tap is made of hardened steel, and can last you many more years as a center punch.
Put the old tap in your lathe / drill press / whatever, and grind it to a 60deg point.
Since this was a pretty short tap, I drilled a hole into the end of a 5/16 rod and inserted the punch.
It works great.