The problem with bows is they really are very hard to use well against moving targets. Even flashy compound bows with sights and pulleys and fuck knows what. They also have a pretty limited effective range. Only take if you're seriously going to train up with it. Also, almost every single trick shot in Robin Hood: Prince of Thieves is impossible. Just a heads up. Remember, bows were used en masse in war, with hundreds or maybe even thousands of archers unleashing simultaneously, raining indirect death from above down on the foe. Furthermore, even more than bullets arrows are designed mainly to wound the torso. The real nasty motherfucker with arrows is when you get one stuck in your guts or lung, and you either leave it in and bleed to death slowly and internally, or pull it out and bleed to death quickly and externally. Zombies quite obviously are not going to give two shits about this. Bows are also impractical for a number of other reasons. To work well, they must be well maintained and dry. This was one of my main reasons for suggesting a semi-auto AK. You're on the run from millions of shambling undead horrors. You do NOT want to have to stop to strip down your gun.
There are several martial arts weapons that would be pretty damn good against zombies. Shaolin spades and glaives come to mind. However, this is only if you're trained in the use. Martial arts weapons tend to be tricky and showy, because that is the whole point of having to master them. It's fine if you happen to know kung-fu, but you can teach anyone enough basics with an axe or broadsword to fight zombies in an afternoon.
Now, talking of fighting en masse, and going back to what I said about my viking re-enactment group earlier, archaic weapons really come into their own if you have a unit of people who can wield them effectively. Fifteen guys trained in dark ages fighting techniques, ten in a shield wall with swords and axes, five with long handled spears, would basically be like a lawnmower that cuts zombies instead of grass. Three men, two with axes and shields and one with a long spear, are the mini version. I've seen such a group fend off eight fully armed, intelligent human opponents in dense terrain (woodland). and zombies ain't gonna be smart enough to dodge. As long as you keep hacking and stabbing, they'll keep climbing over the dead.
For all those suggesting baseball bats, I can't help but think you've hit on another, quite different falsity of media representation. This is the thing in horror films and police procedurals where the human skull is easier to crack than a soft-boiled egg. This just ain't true. A baseball bat will kill zombies, but it is simply not going to guarantee a first hit kill, which is vital. You need a much more concentrated force. Ironically, a cricket bat, a la shawn of the dead, would probably be more effective, but you really want something bladed. Machetes, axes, western swords, maybe a proper mace. In a pinch, a hammer will be far more useful than a baseball bat.