In The Walking Dead comics, the word "zombie" wasn't used at first, but fairly early in the series, it was introduced. Rick initially thought it was too silly to mention, but eventually accepted that it was an apt description of the undead.
I vaguely recall reading a comment on this issue from the franchise's creator, Robert Kirkman. Basically, he said that at first, he didn't want to use the term, but he kept writing "zombie" inadvertently and having to edit it out of every issue. Afraid that he would eventually miss a "zombie" somewhere in the editing process, he finally decided to get it over with so any accidental uses of the word wouldn't be problematic. Still, the word is very rarely used in the comics, despite the fact that the characters have acknowledged that the walkers are also zombies.
On the show(s), however, the word zombie has never been uttered, and presumably never will. I understand the rationale behind this decision: the audience knows what zombies are, but the characters shouldn't, because it helps to intensify the sense that something truly unforeseen, unprecedented, and inexplicable is happening, and the characters have no idea how to handle it (at least at first). Therefore, the TWD television universe is one where zombie movies, games, books, etc, don't exist.