For years, we have assumed that Mars is a dead planet biologically speaking. Mars possesses a very thin atmosphere, only about 1/100 of our atmosphere on Earth. The atmosphere on Mars is also 95% Carbon Dioxide, which is not very friendly to life as we know it. Another problem about Mars is the temperature, most life we have on Earth, even microbial life (which would be the best candidate for life on Mars today) doesn't do so well in below zero temperatures. The average temperature on Mars varies based on many conditions, such as the season and latitude, but temperatures around -50F are very common. Only in the Martian summer are temperatures likely to reach above zero Fahrenheit.
We have concluded that due to too low of temperatures combined with low atmospheric pressure, that liquid water could not exist on the surface of Mars. However, we have seen some evidence that contradicts this recently, and it just goes to show that we don't know everything to know on the subject. In 2008, the Phoenix lander took a photo clearly showing liquid water drops on one of it's landing struts, this liquid water slowly grew over the course of a month. 
The fact that this happened in the northern polar region of mars, in late fall / early winter really is interesting. The temperatures measured by the Phoenix lander during its roughly 120 day mission varied from -20C (-4F) at the warmest to -90C (-130F) at the coldest. The Phoenix mission detected Perchlorate, a type of salt that acts as an antifreeze in the soil, when mixed with water, this would greatly lower the freezing point of water.
Drops of liquid briny water seen on the Phoenix lander.
The next point of interest that I believe could show signs of life on the red planet is Methane. Most of the methane on Earth comes from life, either by methanogenic bacteria or as a byproduct of digestion of herbivores. I think that complex animals are not a likely explanation, as Mars is far too inhospitable. Something very interesting that came from analyzing several years of methane production on Mars is that methane production started in the spring, continued and increased in strength throughout the spring and summer, reached a peak in the fall and died out entirely come wintertime.  The following spring, the cycle starts over again. The methane is also not uniform to all areas of Mars, there are three hotspots where it the Methane is coming from, at Tharsis, Elysium and Arabia Terrae; areas that are near the equator.
The methane is continually being produced, because methane does not last long once it reaches the upper atmosphere. Because of this, the Methane is constantly being produced and replenished on Mars, because otherwise we would not be seeing accumulations of it lasting most of the Martian year. 
The question about whether life is responsible, is another matter. Volcanism would produce methane, but also other gasses, which have not been detected. There could be as of yet unknown geologic processes at work that are producing methane, but why would a geological process change with the seasons? That doesn't make sense. My honest belief is that there are colonies of methane producing bacteria a moderate distance below the surface (a mile or so perhaps) that account for this. While it could be possible that martian bacteria could exist on the surface in certain seasons (see below) I think below ground bacteria are far more likely.
In 1976, the Viking I and II landers arrived on Mars. They carried on board several experiments designed to look for signs of life. Of the experiments performed, perhaps the most interesting of all results was the Labeled release experiment. In this experiment, the Viking lander added a nutrient solution containing radioactively tagged Carbon 14 to a sample of the martian soil. The scientific equipment on the lander then watched for release of radioactively tagged Carbon Dioxide, an indicator that something ingested the nutrient sample and produced the gas as a byproduct. The test was ran by both Viking I and Viking II in different geographical areas, and the test came back positive.  To ensure sterility, the soil samples baked to about 500C (932F) and the experiment ran again with a negative result. This test was a sure sign of respiration.
The positive result of the Labeled release experiment has been subject to much scrutiny, because another of the Viking experiments also searched the soil for signs of organic molecules, and did not detect them. Our scientific knowledge at the time saw no way for the positive result to mean life if no organic molecules were found in the soil. The recent discovery of perchlorate in the Martian soil has brought this conclusion into doubt however, as perchlorate is well-known to oxidize organic molecules when exposed to heat and destroy them, producing other molecules in their place such as chloromethane and dichloromethane. 
Where things really start to get interesting is that chloromethane and dichloromethane were both found by Viking during it's tests, and Nasa determined the compounds were likely contamination from the equipment. At that time, we did not know that the martian soil contained significant amounts of perchlorate that would easily explain why the Viking landers detected these molecules. The technology we had during the Viking mission simply could not provide accurate interpretation of these results, given what we know now. Viking's results have been redone with soil samples containing perchlorate with very interesting results.
Chile's Atacama desert has a few similarities to Mars current climate, first, perchlorate is present there, it is very cold and dry and does have active life. Scientists ran Viking's biological experiments using soil from the Atacama desert and got striking and thought-provoking results. The experiment yielded traces of combusted and oxidized organic compounds, a virtual carbon copy of the results that Viking got on Mars, the very same compounds that Nasa said were very likely contamination from the Viking lander. This proves without any shadow of a doubt, that Viking did detect organic material. 
All of this evidence is highly suggestive that there is active microbial life on Mars. I strongly believe it is possible and hope to see my hopes confirmed in the future. It's an interesting possibility to think about, at the very least. Hypothetically speaking, if it does turn out that there is bacteria on Mars, the next question we have to ask is did it independently evolve there or was it seeded by material ejected into space by an asteroid impacting the earth in the distant past? Both are interesting possibilities. If the bacteria independently evolved on mars, this would be revolutionary to our understanding of life as we know it.