I recently became aware of this type of micrometer, and had to get one. It came with two anvils, one flat and the other a round pin.
This is a Mitutoyo 117-107. The equivalent Starrett is model 220.
I bought it so that I could measure the thickness of a reel end plate without removing the plate from the chuck. The flat anvil fits into places that are too narrow for a standard micrometer, or even the jaws of a dial caliper.
The pin anvil measures the wall thickness of a tube.
North Branch Reels 
The shank of broken end mills makes a dandy anvil if you wish to have one that’s bigger or smaller or if you lose the one that came with it. If you remove the clamp assembly you can use it to mesure a step on a flat surface.
Two good points, thanks. There are also many possibilities for home shop fabrication of special anvils.
Dave
True, though the only one I’ve ever made is a ball bearing on the end of a small shank. I have to remove the radius of the ball bearing from any measurement but sometimes nothing else will work. Make sure you re-guage it (zero) pretty often. With all the bits (clamp, anvil, etc…) reacting to heat and conditions in general they tend to lose their zero much easier than regular mikes.