In this video I show how to make a bolt drill guide, which was used in this video to remove a broken bolt which was deep in a hole- https://www.youtube.com/watch?v=dJfkCj3FWBs
Obviously if you have access to a centre lathe you can easily drill through the centre of a bolt, so this video show how to so it on the lathe and also how to do it using a pillar drill.
Some more videos that might be of interest are-
How to remove a rounded Allen head bolt- https://www.youtube.com/watch?v=WDOWP
How to remove a stripped screw- https://www.youtube.com/watch?v=_mTFQ
How to remove a broken bolt- https://www.youtube.com/watch?v=_R1b8
How to remove a rounded nut or bolt- https://www.youtube.com/watch?v=R5d0B
Screw extractors | Easyouts - https://www.youtube.com/watch?v=SMrDY
Removing a broken bolt using a welder- https://www.youtube.com/watch?v=aRrz-
Remove a broken bolt using a left handed drill bit- https://www.youtube.com/watch?v=FYvaP