Yes definitely. About ten years ago nearly everyone thought it was impossible. Apart from a few such as Gilbert Levin who has maintained all along that he thinks Viking discovered present day life already with his experiment - and some who thought there could be life in caves.

But that all changed with Phoenix in 2008. And with this sequence of photos:

It might not look like much. But it seems to show droplets of some material forming on the legs of Phoenix. then they grow, sometimes two droplets will merge, and then suddenly they disappear, presumably fallen off.

Phoenix had no way to examine those droplets. But the leading hypothesis is that they are droplets of salty briny water that formed on the salt thrown up on its legs when it landed. Probably taking in water from the atmosphere (deliquescing). It's hard to think of anything else that could be liquid in those conditions and the droplets certainly look like some form of liquid.

Pheonix also made isotope measurements of the Mars atmosphere which showed that the carbon in the carbon dioxide was replenished from volcanoes, and the oxygen must have exchanged chemically with something else, presumably water on the surface. That's rather a lot to discover just by measuring the ratio of isotopes for the two elements that make up the main constituent of the Mars atmosphere :).

They couldn't show whether the water is there all the time or only there sporadically. But over periods of millions of years, there is water present on Mars, liquid water, not ice. Could be thin films of liquid but is some there. Could be formed sometimes from volcanic activity or impacts, or could be it is always there.

So that got everyone thinking about it afresh. Because if there is liquid water on Mars, that suggests there might be a chance of life there.

The ionizing radiation is not a problem for present day life if there is liquid water there right now. It is for Europa - the flux of radiation for the Europa is so extreme that any surface life wouldn't have much of a chance not if it is right on the very surface.

But on Mars the level of ionizing radiation is the same as is experienced inside the ISS. The ISS has a problem with microbes like all space stations - they have to be cleared out from the atmosphere, indeed the atmosphere is kept very dry to discourage microbial growth. And that's just ordinary microbes. Radiation hardy microbes wouldn't even notice the levels of radiation on the Mars surface. Harmful to humans - humans are limited to a few years on the ISS because of rules of maximum lifetime radiation dose. But many microbes can even repair DNA damage within a few hours while alive and won't even notice Mars surface levels of radiation.

The reason ionizing radiation was thought to be a problem for life on Mars prior to 2008 was because they thought there was no possibility of water on or near the surface, and so, that any life there would have to have survived in a dormant state for millions of years. A very gentle dose of radiation each year can build up to be deadly for microbes over millions of years. After all that's a million times the dose you get in a single year. And what's more, it works exponentially. If ten million years of radiation is enough to reduce your population of microbes to a tenth, say, of the original, then twenty million years of radiation will reduce it to a hundredth, thirty million years to a thousandth, and so on.

Over billions of years the Mars surface radiation is so damaging that over three billion years it could reduce entire layers of organics meters thick to just water and gases and not much else. That is why we probably have to dig at least several meters, and ideally 10 meters to have a good chance of detecting early life on Mars, dig down deep enough to find deposits protected from surface conditions (or if very lucky, find newly exposed deposits that in the very recent past were ten meters underground)..

But over a period of a year or a century even, this radiation has negligible effects on many microbes. So, as soon as there is a possibility of water there, there is a possibility of life also.

The next discovery was this

Warm Season Flows on Slope in Newton Crater (animated)

This shows a cycle through spring, summer, then finally winter. As you see these streaks form in spring, extend down the slope, get wider, then fade away.

They are not thought to be damp patches as such. But the timing is not correlated in any way with the winds on Mars. It's too warm, far too warm for dry ice. The streaks start to form when the surface temperatures get above 0C on sun facing slopes.

All the models for this involve water in some form. Until recently there was no direct detection of water there. And we still don't have it. The problem is that the spacecraft that takes these photos can only take the photos in the early afternoon, the very worst time of day to spot water on Mars as that is when it is driest. Early morning would be a great time but because of its orbit, which takes it closer to Mars on the sun facing side at the time every day - it can't take those photos we'd like it to take to help solve the mystery. The streaks are also too narrow for the resolution of spectroscopic mapping of Mars.

So, thought we just wouldn't know for a long time. But then recently with careful work, they didn't find water, but they found the next best thing, strong evidence of hydrated salts on Mars in these RSLs.

Now, there are lots of streaks of many types on Mars. Most are caused by things such as land slip, wind erosion, even blocks of dry ice rolling down slopes, and dry ice also forms gullies The RSLs are extremely rare, only a few spots known on Mars where they occur. And other apparently identical slopes don't have them.

Still this very rare phenomenon on Mars does seem, best, even only theories so far, to be caused by water.

Another development, Nilton Renno who is in charge of the REMS surface weather station on Curiosity - a notable scientist with many honours - he and a team of other scientists did experiments involving putting salt next to ice in Mars surface conditions. He found that little millimeter scale droplets of water formed very readily in those circumstances.

"Based on the results of our experiment, we expect this soft ice that can liquify perhaps a few days per year, perhaps a few hours a day, almost anywhere on Mars. --- This is a small amount of liquid water. But for a bacteria, that would be a huge swimming pool ... So, a small amount of water is enough for you to be able to create conditions for Mars to be habitable today. And we believe this is possible in the shallow subsurface, and even the surface of the Mars polar region for a few hours per day during the spring.'"

(transcript from 2 minutes into the video onwards, from Nilton Renno video (youtube)

Curiosity also found evidence of water beneath the sand dunes on Mars, which was quite a surprise. Just a cm or so below the surface and it was indirect evidence - increased humidity as it drove over them. If so, this water dries out in the daytime and is probably very salty - but on the other hand life does have a way sometimes of creating its own micro-environments. Nilton Renno thinks there is a chance it could be habitable though most think it would be too salty and too cold.

Then there's the work of teams of scientists at DLR, german space agency. They have experimented with various lichens and green algae from cold dry places on Earth. They found that some of them, like this lichen.

Pleopsidium chlorophanum collected at an altitude of 1492 m above sea level at "Black Ridge" in North Victoria Land, Antarctica. This lichen lives at altitudes of up to 2000 meters in Antarctica.

They found that this lichen could survive in Mars surface conditions without any water at all. The way it does it is that it is able to collect the moisture from the atmosphere. In the daytime the Mars atmosphere is very dry indeed, goes down to 0% relative humidity. At night though, it cools down so much, that the tiny amount of water in the atmosphere becomes 100% humidity. In the morning you get these frosts that form briefly before the air gets too hot and warm and it evaporates again. Huge temperature extremes from day to night drive this cycle. At night it can sometimes get so cold that dry ice - solid CO2 - would be stable even at the equator. In the daytime it gets well above OC.

Well as it transitions from night to day, then plants like this lichen could get just enough moisture from the 100% humidity of the air to keep going.And they have pigments that protect them from UV light. If they were on the rocks, at an angle to the sun so rather indirect sunlight, the lichens could photosynthesize and metabolize. The fungal component of the lichen, though it needs oxygen, is able to survive too, getting enough supplied by the algae component to keep going.

So - this is quite borderline stuff and lichens are slow growing and the experiments haven't been that long. But the take home message so far seems to be that even in equatorial regions of Mars there is at least a slight possibility that some forms of lichens and cyanobacteria could survive. Bear in mind that none of the microbes and plants tested on Earth evolved on Mars or are specifically adapted to it. Yet some seem to have that capability as indirect result of other adaptations.

Gilbet Levin also thinks that life could be able to take advantage of the early morning frosts in some way, though he doesn't go into a lot of detail as to how that could happen.

His ideas were revisited recently when, looking over the old Viking data, a scientist discovered evidence of circadian rhythms in the experiment. What's more rhythms not synchronized with the temperature cycles induced from outside but offset a little. This seems a quite strong indication of life to some people. If this is right, then Viking already discovered life in the equatorial regions in the 1970s.

This is possible as the viking labelled release experiment is very sensitive. We haven't sent any life detection experiment as sensitive as that to Mars since then. Sadly it was not conclusive because of the unusual and unexpected chemistry of the Mars soil. But it still remains the only experiment sent to Mars that had any chance of detecting present day life at typical concentrations found, for instance, in the Atacama desert core. Curiosity would not be able to find life at those tiny concentrations as any kind of recognizable organics signal because it is just too sparse.

Anyway so where there is water or humidity, there's a possiblity of life. But it depends what form the water takes. Skeptics say that yes, there is water on Mars (we can't deny that after Phoenix's atmospheric measurements and now Curiosity as well) - but that it is all too cold or too salty for life. It could be liquid right down to well below -20C, usually accepted limit for life to reproduce, if it is also sufficiently salty. So liquid water doesn't prove it's habitable.

So - nobody knows. But on the other hand there are many potential habitats on Mars. And even if many of them are inhospitable to life, too cold, too salty or whatever, it just needs one of those habitats to pan out to make Mars habitable to life.

Some skeptics will tell you that the Mars soil is too poisonous for life because of the perchlorates. But perchlorates are most poisonous at higher temperatures than on Mars. Poisonous to humans certainly. But some microbes actually use perchlorates as food. So it could even be an energy source for Martian life. The perchlorates don't seem to be an issue, and may indeed be an extra habitability factor for hardy mocrobes.

For more details about these potential habitats see my Are There Habitats For Life On Mars? - Salty Seeps, Clear Ice Greenhouses, Ice Fumaroles, Dune Bioreactors,...

For the new ideas about the Viking labelled release experiment and the possibility that they may have detected life back in the 1970s after all, see Rhythms From Martian Sands - What Did Our Viking Landers Find in 1976? Astonishingly, We Don't Know

For the hydrated salts discoveries for the RSLs see Why Are Hydrated Salts A Slam Dunk Case For Flowing Water On Mars? And What Next?

For more about why cosmic radiation is not lethal for life on Mars on the surface if these liquid water habitats exist, see UV & Cosmic Radiation On Mars - Why They Aren't Lethal For The "Swimming Pools For Bacteria"

And I have many other articles up about related topics as well as quora answers.