A well-meaning -- but obviously naive -- young friend of mine wears a t-shirt with the logo "Jiu-Jitsu Kills Zombies."
This is dangerously wrong and will get you killed.
Jiu-jitsu is an awesome martial art against mortal opponents, but there is nothing in the arsenal that will handle the Undead menace. Zombies do not feel pain. They do not need air. And they will still keep coming after you on shattered joints.
Worst of all, Jiu-Jitsu requires the expert to close with and grapple the zombie. This is exactly where the zombie wants you: close, where his teeth and claws can do their damage. And let's not forget that this will mean prolonged exposure to the zombie's bodily fluids, which may infect you. We certainly shouldn't forget that getting caught on the ground with a zombie is a recipe for disaster when his friends stumble onto the scene.
I was trapped in a bar once by some dork who talked my ear off about how his Ninjutsu was awesome and most certainly zombie proof. Please. Ninjutsu? This isn't Naruto, you mouth-breather. Smoke bombs and hiding in the trees isn't going to help you one bit against zombies. Although I admit all bets are off if ninjas face off against zombie pirates.
Ninjas may be able to hug tree limbs for hours, but time means nothing to the Undead. They'll just mill about the roots of the tree until your mom calls you home for dinner. And what ninja doesn't still live in his mom's basement?
So what martial art does work against the walking dead? Have you seen the Filipino Martial Arts? Variously called escrima, arnis, or kali, Filipino Martial Arts start the new student using two foot long sticks. But those sticks are representations of -- and soon replaced by -- giant jungle knives! You'll quickly learn moves that will help you lop off limbs, eviscerate corpses so they trip over their own guts, and stop 'em cold with decapitations or bisected brains.
Going hand-to-hand with the shambling hordes is unwise. Wrestling around with them is suicidal. Unless you're Chuck Norris, I strongly advise you to use weapons and learn to use them correctly.