If/when the zombie apocalypse comes, the answer is simple - find a way to get refuge on an island that hasn't been infected with the zombie virus!! Zombies can't swim, right? Ugh I have got to stop watching reruns of Walking Dead episodes after it gets dark out.
July 20th, 2012: Never forget the day the fb douchebags tried so hard, but ultimately failed. Viva la October 2011! Yeah, I called you douchebags.

BFP 1/18/11, EDD 10/1/11. Born at 37w5d on 9/15/11.
***BFP Chart***
"There will come a time when you believe everything is finished. That will be the beginning.
Re: I had a dream it was the zombie apocalypse last night. And a revelation...
This is true, but doesn't running take a lot of complex movement as well. I will agree that swimming is more difficult. It would depend, as you said, on what type of zombie we're working with here. If they're the slow walking-will-get-there-eventually-and-kill-you kind, then I would say no to the swimming aspect. But if they are the kind (as they all seem to be these days) that runs and hunts you down, then maybe swimming could be possible.
Also consider the quality of the tissue you're starting out with. If it was a sedentary person who was severely out of shape, then maybe they're not a good candidate to be a swimming zombie. But, if you happened to be a marathon runner, Olympian, or triathlete, then maybe you have a shot at being a swimming zombie.
Which brings another question to mind - how strong is muscle memory? Maybe zombies can only perform certain functions that were once part of their basic instincts. So the majority of them can run quite well. Well, by that same logic, if Michael Phelps were to become a zombie, his zombie self would possibly function better in the water.
I have to bring up something else here: sea life. I'm really having trouble remembering here, but on land I would assume animals tend to avoid zombies? Maybe it's the general smell of death and decay. Some animals go for that, though. Well in the ocean, you can bet that bloated floating zombies would eventually be nibbled on by curious swimmers-by.
But yes, I'm sure some would eventually make it to people-inhabited lands, after circulating for a while.
I agree, Australia is probably a safe bet. You could set up a secure fortress for the human race to hunker down and propagate. The only problem is, this continent is famous for having the deadliest animals. Still, better to die from a snake, scorpion, box jelly, or duckbilled platypus than a zombie.
It would make a great TV show, though.
BFP 1/18/11, EDD 10/1/11. Born at 37w5d on 9/15/11.
***BFP Chart***
"There will come a time when you believe everything is finished. That will be the beginning.
Oh and I Love all of this. You think like me. One thought after the next lol.
All of this makes sense. Except salt water (and sun) is pretty erosive. It may erode the zombies before they get to you, even if the sharks don't get them.
I would probably go to a smaller island than Australia because Australia is populated. I would want to go somewhere where I can pretty much know everyone, so if it comes down to it, We can get rid of the zombies fast. Does that make sense?