Here's a short list of several potential zombie killers. If anybody can think of anything else, feel free to post it in the comments section.
They tend to be big and heavy, and the blade likes to get stuck in zombie skulls. If you miss a swing, it throws you off balance, leaving you open to a zombie bite. Since the handle is made of wood, it might break, leaving you weaponless. Overall, not a great zombie weapon. On the plus side, it has a fairly good reach, and has uses outside of combat, such as chopping down trees and doors. Not my number one choice for zombie killing.
Hatchets, tomahawks, and other hand axes are small, lightweight, can be used for various camp side activities such as chopping wood and zombie brains. Downside is that is has a short reach, and like its big brother, hatchets get stuck in zombie skulls very easily. You could find something better, but overall, not a bad weapon.
These are great zombie killers. People have been using them to hack each other to pieces for years now, so using them on a zombie shouldn't be very different. Just be sure to aim for the neck, and be careful with the heads. They can still bite. Also double as tools, and are useful in wooded areas.
Kitchen knives, Swiss army knives, and cheap pocket knives from Wal-Mart are going to be next to useless. If you have a half-decent knife, that's better, but you're better off using your knife for more mundane tasks, like cutting your food, rope, or your wrists (God Mode is not suggesting you commit suicide. However, death may be preferable to zombification). Not very good for killing zombies. Better than nothing though.
Lightweight, portable, and many are made of solid steel with a rubber grip. Great for bashing skulls in. Be careful with it though. Since it has a short reach, you may have to get closer to Zed than you may like. Useful for putting up a barricade.
They can destroy just about anything in your way, including a zombie. But they're heavy, and a miss will throw you off balance. Also, carrying them along with the rest of your gear won't be any fun.
Most people think a crowbar is the ultimate close quarters weapon for taking on zombies. It can cave in a zombie's skull in a single hit, is relatively lightweight(especially the titanium models), and can still open doors, crates, car trunks, etc. However, they are NOT designed for swinging at anything. They're uncomfortable, unwieldy, and not very balanced. A pry bar is a little lighter and can accomplish most of the same tasks, and are a little lighter. Still a very good zombie weapon.
Useless. They're loud, require either electricity or gas to work, and aren't very good at killing zombies. Avoid at all costs. Yes, this includes the chainsaw.
They're decorations. Use one, and I can guarantee you're zombie food. You wouldn't use a chair to kill a zombie, would you? Then don't use your $20 katana you bought at a flea market.
Real Swords, Spears, etc
Most things in this category would be great zombie killers. Downside is that they tend to be large, require training, and can't be used for anything other than zombie killing.
While on the internet a couple days ago, I found something a think would be the ultimate zombie killer. Downside is that it's nine pounds. There's a smaller version that's only five pounds, but either one would kick ass. Also very useful for breaking down walls, prying open doors and car trunks, and just kicking zombie ass.
The 18" model