Well, to a degree "more than surviving combat" is what you put into it... But here's some good ones I own and have read or used.
All Flesh Must Be Eaten uses the Unisystem like most of Eden Studio's games; it has a large number of supplements for everything from kung fu zombies to wild west zombies. It's a toolkit game where you can make the zombies work in a variety of different ways. It's the biggest zombie RPG. They are ruthless, I see that there's a WWII (Band of Zombies) and a pirate sourcebook (Arrgh, Thar Be Zombies) coming out this year. So it's well in print. I've played many one-shots of AFMBE and it's a good game. It's crunchier than most indie games but very low crunch compared to the GURPS/D&D/etc. set. But it's pretty trad in that relationships and whatnot aren't really modeled integrally in the system.
(Naturally you can run zombie survival horror in anything from D&D to, well, anything and someone probably has...)
There's a Savage Worlds based game called "War of the Dead," it's sold in some kind of chapter by chapter format that I don't understand. Zombie Run was a good earlier Savage Worlds setting, it focused on the moving cross country aspect that movies like Zombieland and parts of other movies use. I have an adventure called "Weekend Warriors" that is a military vs zombies scenario for SW too. You might choose this game if you already like Savage Worlds in other venues, it's a light trad game.
In terms of deeper story, there's a number of indie games I own that bring some additional dimensions to zombie survival horror.
There's a new zombie survival horror game by John Wick called The Shotgun Diaries that was up for an Indie RPG award. It's been reviewed glowingly from various sources. It's very short (18 pages), not for someone that wants loads of rules support.
There was an interesting zombie game that got runner-up in the 2007 Indie RPG awards called simply "The Dead," whose tagline is "A role-playing game about death and relationships." It is free for download. It focuses on relationships between survivors and how those give people each other strength (or weakness). I downloaded it at the time and was impressed, it's short (32 pages) but the relationship aspect is really neat.
There's a new post-apocalyptic game by Vincent Baker called "Apocalypse World" that's like 300 pages and well spoken of. You'd have to add zombies, though someone is working on a hack for it called "Dead Weight" that does so already... It's got a lot of support right now in indie circles (even if some if it is a little on the rabid fanboy side).
Adding zombies tends to be easy. I'd first go for what kind of apocalypse you want. A Twilight:2000 kind of WWIII military action thing with crunchy rules? A Road Warrior type like Atomic Highway? And then toss in zombies.
There's Left 4 Dead hacks for Savage Worlds, nWoD, and even 3:16 out there too.
Heck, I have a couple zombie-RPG PDFs I don't even know how I got... The RPGnow Haiti relief bundle maybe... Zombocalypse, Contagion... It's one of the most covered genres in gaming. Do you want lots of support or just good one-shot fodder? How much system do you want?