Well, I have to admit but I love the undead. No, not that way ..you're gross! :)

I know of some books and boardgames that feature the grey shamblers, and would love to hear from you about it. What other sources you can recommend for zombie-fans to get their kicks?

First off, I'd like to recommend Max Brooks books "Zombie Survival Guide" and "Z-Day". Especially the later one is a great read, but also frightening authentic at some times.  It gets you scared of the idea to ever run into zombies and pictures the scenario of a full war against them. 5/5 

I think you mean World War Z, not Z-Day right? I still have yet to finish the book (bad habit) but so far what I've read is pretty damn good. There are quite a few other books out there but I haven't read any of them yet. There's a pretty awesome comic series called The Walking Dead that I think is still going, I have the first trade paperback and it's definitely worth checking out.

There's also the Zombie Day event that takes place in certain cities, the only one I've read about and seen vids of was the one in San Francisco. I think there are some other worldwide group gatherings like this out there but I don't know too much about them.  Search for Zombie Walk, Worldwide Zombie Day, and Walk Like A Zombie Day.

Read this, it is quite interesting: http://www.cracked.com/article_15643_5-scientific-reasons-zombie-apocalypse-could-actually-happen.html

The board game Zombies!! is awesome! I love that game...

Already been said, but World War Z is amazing.
 
I'm also a pretty big fan of "The Morningstar Strain" series. The first book is "Plague Of The Dead", and the second is "Thunder And Ashes", and a Third (And final) coming out soon is "Survivors". Sadly, the author died a while back in (I think) December. Sucks hard that the author died, but the books are really good. No guarantee that the final book will be published though, which would be a damned shame. Still, get both.
 
I love the "Slow/Shambling" zombies waaaaay more than say, the Left 4 Dead or 28 Days/Weeks later versions. The Morningstar strain does it really nicely, while alive and infected they act like "Fast Zombies" or Rage zombies, then they die and return as the slow shambling ones.
 
"Day By Day Armegeddon" is also pretty cool, and another, I think it's called "City Of The Dead", is alright.
 
Edit: Looked more into it, and Z's parents (Morningstar Strain series) are in the process of reading through and putting together versions of the final book. Some great news.