While it's not very Walking Dead-like, I definitely recommend playing Fallout (1, 2, or New Vegas. Skip 3.

). If you're looking for a non-linear, story-driven game, you won't be disappointed. And thanks for reminding me I've been neglecting this playthrough of Fallout 1. Other good story-heavy RPGs are Deus Ex, System Shock 2, and Planescape: Torment.
If you want something a little closer to The Walking Dead (i.e.: limited gameplay with the focus on a ridiculously emotional plot), I suggest
To The Moon and
Katawa Shoujo. The latter is free.
Oh, and there's Spec Ops: The Line. At first it seems like a normal run-of-the-mill military shooter, but then it takes an...interesting direction.