UrbanDead

"Urban Dead is a browser-based, grid-mapped, free-to-play multi-player game where you play the survivor or victim of a zombie outbreak in a quarantined city centre."
http://www.urbandead.com/

That picture isn't me, BTW, it's someone without any combat skills.
I have two characters, both are very high levels, with all of the survivor skills, and many zombie skills.
If you die as a survivor, you can stand up as a zombie, and can be "revivified" with a needle, unless you have the brain rotten skill.
One of my characters is in Caiger Mall, which is currently the site of an epic battle (900 survivors in my quadrant of the mall alone.)
It's free, and you use action points (AP,) which regenerate, one per half hour.
It's kinda slow pitched, and can be boring, but it's free, and I'm in a team with 15 others.

I have never heard about that game before your post Axeman

well not so bad game even it hasn't any great graphics or sounds and it is maybe bit slow to play but its fine to me... used to play runescape