A drone plane has been considered, although the technical feasibility isn't really there. Mars has less than 1% of the atmospheric pressure that Earth does, so a drone would have to fly very fast to get to proper lift. This comes at a high energy cost, which would be hard to provide in a lightweight package. Additionally, the plane would have to land at night and do so autonomously.
Even if all of this was achieved (and it is by no means impossible), the drone wouldn't really provide more data than the satellites in orbit already do. Aerial survey is pretty much taken care of, what is needed are actual samples of minerals on the ground.
However, if people were able to go to Mars, some sort of drone would be ideal for real-time surveys and control. The explorers would be able to recharge the drone at will so power isn't too much of an issue. There are ideas floating around that talk about a drone that kind of acts like a grasshopper: it takes in Martian atmosphere, and uses it to 'jump' around the surface. It then lands and takes samples, and recharges its energy for the next hop.
I believe that most UAV designs for extra-terrestrial missions are designed around the use of airships rather than more traditional airplane or quadrotor designs. An example of initial research in the area is the Titan Aerobot [1]
Much though I love the idea of extraterrestrial airships, wouldn't an airship be even less effective than heavier-than-air machines in an incredibly thin atmosphere like Mars'?
Airships would be harder to make work on Mars, but once you have it working you would almost certainly be in a better position.
Also, Wolfram Alpha peggs the air pressure at 39km on earth, the height Felix Baumgartner jumped from, as 330 Pa. It has the atmospheric pressure on Mars (presumably the average at the surface) as 650 Pa. So balloons that will float in that, at least at a low altitude, are not beyond our engineering grasp. (and unmanned balloons on earth have gone down to as few as 55 Pa http://en.wikipedia.org/wiki/High-altitude_balloon).
You are very right - I forgot to mention those. They tend to be a lot more feasible than fixed-wing aircraft, and their ability to land and take samples makes them even more useful.
The pdf was a fun read. Thanks. Don't know where did you get the figure of 35kg though. The article talked about a payload of 12kg if the balloon is filled with NH3. My estimation is that the payload can be increased to about 60kg if hydrogen is used instead, assuming the Mars does have plenty of water. With a bit of more creativity, that figure can be improved even further.
I had at first put the 12kg max from the first figure, but on re-read I saw the water vapor pressure could have a balloon go as heavy as 35kg. It would makes sense that helium (or more preferably hydrogen) would work better. I suppose I should RTFA better next time.
"if Helium is used instead, assuming the Mars does have plenty of water."
I think you mean hydrogen? Assuming we can make a rover that can collect non-trivial amounts of water (say by baking it out of the dirt), we could make a hydrogen filled balloon with electrolysis.
Even if all of this was achieved (and it is by no means impossible), the drone wouldn't really provide more data than the satellites in orbit already do. Aerial survey is pretty much taken care of, what is needed are actual samples of minerals on the ground.
However, if people were able to go to Mars, some sort of drone would be ideal for real-time surveys and control. The explorers would be able to recharge the drone at will so power isn't too much of an issue. There are ideas floating around that talk about a drone that kind of acts like a grasshopper: it takes in Martian atmosphere, and uses it to 'jump' around the surface. It then lands and takes samples, and recharges its energy for the next hop.