http://www.mangareader.net/i-am-a-hero
I think this is the best zombie themed manga I ever read (even though zombie manga seems to be very rare).
I didn't even know it was a zombie manga when I started reading it, I just picked up a random horror manga. Won't get too much into it to avoid spoilers but there's only subtle hints that something is happening until halfway into the first volume (maybe even more than halfway, didn't notice) where you then realize "oh. zombies :D".
I really like how most of the first volume doesn't even deal with zombies and is instead character/plot development with the zombie outbreak only being hinted at in the background (try finding them, now that I know it's a zombie manga I should re-read it and see if I can pick up more) and might even pass off as a completely different story.
Unlike most zombie stories this takes place during the outbreak, rather than suddenly being in a post-apocalyptic world where zombies are dominant, and you see the change take place.
I suggest it for any zombie fans.
[SPOILER="Spoiler"]Technically I don't think we can call them zombies, it's more like an infection and it's much faster acting than zombification, almost instant in some cases later on in the manga, but it's the same concept as zombies.[/SPOILER]