The below gun is a pretty cool looking modern recreation of an axe gun. The short gun barrel and short axe shaft make both weapons a lot less effective than they could be.
I suspect that the original axe guns were made more for decoration than for war. The armory at Castle Eltz in Germany has a couple of axe guns (scroll down) on display.
[Hat Tip: Reddit]
[ Many thanks to Abraham for emailing me the link. ]