I Am a Hero is not your average zombie manga - it's best compared to other horror zombie books/movies that have become so popular recently.
I am a Hero focuses on your everyday character, no one special, as is common with most zombie stories. A zombie outbreak occurs in Japan, and he tries his best to survive.
What sets this apart from regular zombie manga is that:
1. This manga manages to terrify you even though it's still (it scared me more than some zombie movies) and
2. The emotions that the artist conveys are great.
The artist draws the zombies in a very gory fashion - if you don't like that, then this is not for you. However, if you do like gore, it's everywhere in this. The zombie deaths are great, and while some may say that the story moves too slowly, (it isn't overly action-packed) every chapter is needed, either in developing the characters or developing the knowledge of the outbreak.
In summary, this is a great manga if you want to scare yourself and gain a full understanding of the outbreak. If you want more action/fan service, go read Highschool of the Dead.