No, seriously, it is possible. Where there is water, on Earth, there is life. And given we know Earth and Mars have traded bits of meteorite fragment over the ages, and the tests NASA has run on various germs and spores, the odds are good that either life evolved first on Mars and got here, or earth-borne life has already gotten to Mars.
Any way you slice it, if life’s been clinging on there, it could have evolved in ways we can’t predict but that might make our immune systems very, very unhappy. Whether zombies result is another matter, but….
On the other hand? Earth and Mars have traded bits back and forth. So I’d say that if there is life on Mars, it’s at least as possible our immune systems have already met and munched on the invader sometime in the ancient past. Who knows?
Long story short – we should colonize Mars. Carefully. Just in case the Doom movies are right.