Kikimaru said: But they do risk chipping or breaking.
Depends on the quality, but modern swords can take a lot of abuse before breaking. How much is up to the exact grade of steel and the type of heat treatment, but modern metalurgy is in general far superior to that of the past.
Chipping is a result of Japanese-style hardening techniques, while through-hardened blades have more durable edges but aren't quite as sharp. Personally I'd go with one of those in a scenario like this.
And if those zombies still have blood (v. likely), you have to keep cleaning it or it will start to rust.
Guns need maintanace too, though, and swords are actually rather easy to clean. Plus, a bit of rusting isn't really going to reduce its killing power or make it dangerous to use. I don't know much about guns but I imagine they are more sensitive that way.
Also, didn't the ZSG mention a Roman Gladius to be a more effective sword?
Some people swear by the gladius, but I would not like to engage a zombie with any blade shorter then 25", honestly. Also, the gladius is primarily a stabbing weapon that really isn't designed to take on zombies at all.
Hype and legends aside, the katana is actually a sensible choice - they're not too cumbersome but tend to be compact and pack a punch, and are designed to deliver dismembering cuts which is exactly the kind of damage you want to do to a creature who needs muscles to move but can do without most of its vital organs.