This series is one of my favorite online games in general. The Sonny series is honestly about as good as other games currently on the market. It's a full RPG with a series of arena-style fights. I will admit that the zombie aspect might not be what you expect. It uses a system of turn-based combat and often features you fighting non-zombie opponents. This isn't just a zombie slaughter game.

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Your character, Sonny, is a zombie but you are more of a mutant than a traditional zombie. Sonny 2 lets you take 3 separate paths of zombie development though and you can choose to be a berserk killer.
Regardless, it's a fun game with a standard zombie story. Sonny finds himself on a yacht with a bunch of zombies killing everyone. He escapes the zombies and the top secret government clean up team and he must now find a tape player in their dystopian world to try and find the truth behind what's happening.
The real draw is the gameplay though. The fighting is in depth, there's a lot of room for strategy and varied gameplay, the AI is surprisingly good at outsmarting you, and there's just a lot you can do in the simple turn based setup.