It's all about figuring out what kind of organisms can survive what kinds of conditions. Looking to known extremophiles on Earth, we've got little critters living in boiling hot springs in Yellowstone, thriving in the saltiest lakes in Utah and cheerfully metabolising away in Antartica. If they can live under such extreme conditions here on Earth, why not elsewhere?
Life on Mars? Still possible in microbial form. While the radiation-scorched surface where water can't exist in liquid form may appear quite inhospitable, the potential for liquid water below the surface still exists. Life as we know it needs water. We know water ice exists on Mars and water vapour has been detected. Extremophile organisms could dwell underground, or even in the polar ice caps.
And Mars might not be the only place in our Solar System that could host microbial life. Jupiter's moon Europe and Saturn's moons Titan and Enceladus have conditions that might be favourable to extremophiles.
Hardcore: Astrobiology and Extremophiles
Where do you think the most likely place to find extremophile life is on Mars? What kind of extremophile?
Her Grace has spent a wee bit of time in the field of astrobiology, probably the best use of those Cell Bio classes she took her Freshman and Sophomore years at university.