If we assume that life got started during the warmer, wetter conditions of Mars' past, could it still be hanging on somewhere under its frigid, sparse atmosphere? Without a careful examination of hundreds of potential habitats around the red planet, that question is probably impossible to definitively answer. But we can get a sense of whether that's possible by examining life in extreme conditions on Earth.
In the latest effort of this sort, an international team of researchers have taken samples from deep in the Siberian permafrost and put them under conditions similar to those on Mars: freezing, low pressure, and devoid of oxygen. Despite the unpleasant environment, several clones of bacteria grew out. A bit of study showed that they were all relatives of a strain first found growing on refrigerated, vacuum packed meat.
Although this doesn't tell us about what might be growing on Mars, it does highlight a bit of danger. We can contaminate the red planet if we don't carefully clean the hardware we send there.