Angry zombies spawn frequently in magical biomes, and occasionally in any biome, among the usual nighttime spawns.
They have extra health and well as boosted damage compared to normal zombies. There are even Angry Zombie Villagers who can be cured the same way as regular Zombie Villagers. When killed, they drop more rotten flesh than normal zombies and are almost guaranteed to drop a zombie brain.
They have glowing red eyes, and look all-too similar to their "big brothers", Furious Zombies.