Continuing the derailment - Zombies, you need to read the book Day By Day Armagedon. Simply the best zombie book ever.
You never want to use a blade on a zombie.
Sounds like the start of a new thread
If I didn't have a trusty 12 gage with 00 magnum shot (or have run out of ammo because there are too many freaking zombies), then a fire axe should do nicely. If there was enough time to prepare, a (real) katana or polearm should give you the reach and ability to decapitate zombies before they can shuffle into grappling range.
Like the bayonet, there are probably lots of great alternatives to swords and polearms, but unless you are willing to lug around a flamethrower or destroy entire city blocks with thermobaric weapons, something smaller, lighter and always at your side is probably prefferable.