None of my characters normally wield an axe, but there were several axes I liked, particularly the double-sided axes such as the Heavy Iron Axe and the Elven-steel Axe. I can definitely see a dwarf guardian swinging it side-to-side through a crowd of clamouring goblins. Also useful for chopping wood for a campfire - and showing off your battle prowess to your comrades while drinking ale and singing loudly and badly - another favourite past-time of dwarves.
Heavy Iron Axe
Amongst the other axes, the Thain's Axe, Westfold Axe and the Axe of the Mark are quite detailed and interesting. The Axe of the Rider and Wildermore Axe are also unique.
Axe of the Mark
Oh, and there was also one that was unbelievably ugly ... the Sellsword's Axe. It reminds me of someone doing the sign of the horns, but with a blade along one edge. Maybe the weapon was supposed to be particularly good at warding against the evil eye (Eye of Sauron) and killing his minions? It does Westernesse damage, which is strong against The Dead, Unseen and Gaunt Men. Coincidence? Probably not.