The good news is DayZ is a really interesting zombie survival game, with persistant characters and inventory. The bad news is its actually a mod for ARMA 2, and you will need both ARMA 2 + ARMA 2: Operation Arrowhead to play it (aka ARMA 2: Combined Ops.)
The mod is currently in Alpha, there are many bugs, the servers might go down 4 times an hour for updates (or stay up for hours, it depends), and you will probably get frustrated with something at some point, no matter who you are.
But, and there is a but, despite those issues, and despite being early in development there is something really compelling about this mod. It might just be that zombie survival game you've always wanted.
You start out at a random spawn point with a revolver, and some basic supplies. You will have to scavenge better weapons, ammo, food and fluids, and medical supplies to survive. All of those things will be found in enterable buildings, where you will of course also encounter zombies.
For me this creates a very interesting tension, whereby you would be best served by staying away from those populous areas, but really you need what is there and have to risk yourself to get it.
Here is Prt 1 of a fun video series on youtube:
Its suggested you use http://www.mediafire.com/dayz to dl the files. Instructions in the readme :)