Byrnal Haley decided to change the plugs in his '89 XJ-S convertible.  He put his wrench on the first one, and couldn't get it loose.  He then tried harder, and the spark plug broke off.  At this point he decided he clearly didn't know what he was doing, so he had the car flatbedded to his mechanic -- who broke off three more!

Obviously both Haley and his mechanic are applying obscene amounts of torque.  Or, maybe not.  Here's the half a plug Byrnal ended up with:

Yes, this is a "V-Power" plug, hence the little V notch in the center electrode.

Remember, the hex is 5/8", not the 13/16" found on most plugs.  This thing is small.  The fracture surface is really small.  It's an annular surface, about 9/16" OD and 1/2" ID.  The cross-section is therefore only about 1/32" across.  It broke extremely cleanly.  Honestly, the thing looks like it was designed to cleave here.

Once they broke, the mechanic was reportedly able to get them out with an EZ-out without further ado.  This makes sense; since the entire center section of the plug comes out cleanly there's no need to drill, just jam the EZ-out in there and start turning.

Byrnal suggests it'd work even better if you heat the head and then chill the plug, perhaps with compressed air or CO2 or maybe just an ice cube.  Dunno how you'll heat the head, though.

Folks, these plugs don't get stuck because some jerk installed them with a 6-foot breaker bar; if he did, they'd break off during installation!  Please get this through your head: steel threads will seize in aluminum if you don't use anti-seize compound.  And get it through your mechanic's head, too.