There has been much deliberation regarding the possibility of life on Mars. Four major examples that come to mind are the fictional stories written, Schiaparelli's discovery of canal like features on the face of Mars, Percival Lowell's assertion these canals were built by an ancient intelligent race and the recent discovery of certain formations and compounds found in Martian rock. Two of the more well known science fiction works are H.G. Wells' "War of the Worlds" 1898, Ray Bradbury's "The Martian Chronicles" 1950. I'm sure an important influential factor was Schiaparelli's discovery of what he called the 'canali' or canals in 1877. "...On balance, he favored the view that they were natural waterways, although he never opposed the suggestion that they might have been intelligently constructed..." http://www.daviddarling.info/encyclopedia/M/Marscanals.html Percival Lowell took the discovery of the canali to the next level. "...Starting in the 1890s, the wealthy astronomer Percival Lowell saw what he thought were straight lines crossing the surface of Mars. While he was not the first to see them, he was among the first and most vocal to make the radical interpretation that these lines were much too straight to be natural features. Therefore, they had to have been built by an advanced intelligence..." http://www.setileague.org/editor/marsface.htm (this is a really great link - lots of info!) The modern-day debate is over the discovery of strange formations as well as what might be organic compounds present in martian rock. Scientists are trying to determine whether or not these features are possibly signs that there may have been life on Mars. -http://mars.jpl.nasa.gov/life/ --http://mars.sgi.com/MPF/martianchronicle/martianchron7/signs.html So, if you mean the little green men of our imagination, it probably started around or near the discovery of the planet itself (which is difficult to determine as no one knows who first disovered the planet). Realistically, the idea of possible simple life forms inhabiting Mars, maybe since the late 1970's.

Just to add a little to what has already been said. The mindset of the time seems to have already been primed for the possibility of life on other planets, perhaps because the recently popularized (by Darwin and others) theory of evolution made it seem inevitable. Mars was most readily observable, particularly given the astronomcal equipment of the time, and in many ways seemed most earthlike. The nature of its atmosphere was still "up in the air". (Sorry, that didn't register with me as a pun originally, but then I couldn't stop myself.) Schiaparelli described "canali" which might have better been translated as "channels", but which of course was translated "canals", in a lazy or unskillful handling of the Italian. He didn't initially propose that they were artificial, but in the English-speaking world, canals are man-made objects, and some spectacular earth-bound projects had recently been completed (Suez, 1869) or attempted (Panama, 1880). Lowell's imagination was fired, and Schiaparelli's own imagination may have gotten caught up in the fervor later. Now, of course, it appears that what Schiaparelli, Lowell, and others saw--while others didn't--was an optical illusion which was assisted by psychological suggestion. It came along at the right time to capture the popular imagination, not to mention that of a number of authors. This comes from several sources, but I liked this summary: http://www.theguardians.com/space/orbitalmech/gm_emoi1.htm

Mars is the only planet besides Earth that was ever cut by flowing water or graced by lakes and ponds. Now, that water is frozen at the poles and buried beneath Mars' frigid deserts. In those ancient martian pools, might life have sprung up and prospered? The pools are dry and sterile today, but could life persist in deep and hidden places? Someday, will humans walk those distant deserts, seeking signs of ancient life? http://www.lpi.usra.edu/expmars/edbrief/edbrief.html Life on Mars? It’s a debate that has raged since the late 19th century, when Italian astronomer Giovanni Schiaparelli trained his telescope on the Red Planet and concluded that the canali he saw on its surface were the transport routes of an advanced race. http://www.commonground.ca/iss/0510171/cg171_geoff.shtml The ancient Greeks and Romans believed there was life on Mars. Today we know there's evidence of water and where there's water there's life.