That was a lot of fun! I tried to think of a movie where Mars is actually depicted correctly as it is now: low gravity, cold, almost no air. I couldn't think of a single movie where that happens. I went on Twitter and asked the folks who follow me what they thought, and got lots of suggestions. Unfortunately, no movie suggested that I had seen was entirely accurate.
"Mission to Mars" was close, but they had a dust devil pick up astronauts and even tear one in half. Granted, it's implied that was an outcome of alien tech, but dust devils on Mars simply aren't that strong. Also, that movie got so much science wrong I don't really feel like cutting it much slack.
Most other movies forgo showing Mars's 0.38 Earth gravity due to the difficulty in portraying it well. Some, like "Robinson Crusoe on Mars" - which I loved as a kid - gives Mars enough air to breathe if you take oxygen supplements. I'll note that I also just saw "John Carter" and actually quite liked it. I knew it was epic, sweeping fantasy going in, so I was able to not worry too much about the scientific booboos.
Doctor Who has had several episodes take place on Mars including the recent "Waters of Mars". That too was close - the Doctor was in a spacesuit - but gravity was clearly Earth-normal. Sigh.
A lot of people suggested "Watchmen", but only a few minutes were on Mars, and the gravity was unclear. Also, I suspect that Dr. Manhattan could've manipulated the gravity, so it doesn't really count.
At the end of the show, Annalee challenged HBO to make a good Mars series. The obvious place to start is Kim Stanley Robinson's Red Mars trilogy. And unlike Game of Thrones, they wouldn't have to wait for more books to be written!