In Disgaea series, you could create your own army of zombie undeads as your party member. But do remember that they're not very reliable, since they got low defense and slow speed.
In Metal Slug, your character could be infected by zombie enemies. In zombie state, your character was slow and less agile, but their offensive power were greatly boosted.
But TBH, it would be hard to play as a "good" zombie, since you're basically the "bad guy" due to your circumstances (no intelligence, consume raw meat/brains/etc, highly contagious).
Lastly, there was this interesting mechanic in the old RE: Outbreak online mode, where your character could become a zombie if their T-Virus gauge reaches 100%. And the best part was you can still control them, even after they had turned into a zombie. So you can either help your other teammates, trolls them, or hunt 'em down, which was your main objective as a zombie.