But I spent a whole afternoon thinking about it, just to see if it would be feasible. It might be wasted effort, but just imagine how cool a space probe on Mars would be if it could fly through the atmosphere like here on Earth!
I had to look up a couple things. First of all, the gravity is lower, which is good. It's about 3.7 m/s2 as opposed to 9.8 m/s2 here on Earth. However, the Martian atmospheric density is only about 0.02 kg/m3, and here on Earth we're blessed with a thick 1.2 kg/m3 atmosphere. Atmospheric density is essential to lift (L=1/2CLrv2A), so if you have a density that is 1.7% of Earth's, you're going to get lift that is 1.7% of what it would be on Earth.
But I had fun brainstorming anyway. My initial idea was to have a solar powered plane similar to the NASA Pathfinder or Helios unmanned aerial vehicles. The Pathfinder weighs about 930 N on Mars, so you'd need at least that much force in lift, prefferably more because you have to lift off the ground. I played around with FoilSim, and the highest lift coeficient I can get is about 5. I then picked a realistic value for the velocity, just to see what ball park I'm in. On Earth the Pathfinder doesn't go much faster than 7-10 m/s, so I plugged 7 in. The result: 173 N. Definitely not going to cut it.
What really puts the nail in the solar-powered coffin is that the lower density means the propellers on such a craft would be completely useless, so you wouldn't be able to accelerate to 7 m/s to begin with. Oh, and another thing. The Sun is much further away, so the solar arrays won't get as much energy.
Where else can you get free propulsion on Mars?
I read somewhere that you could theoretically manufacture rocket fuel from the Martian atmosphere. Mars' atmosphere is 95% Carbon Dioxide, so you could make methane with the following reaction:
4H2 + CO2 --> CH4 + 2H2O
The problem with this is that you would only be able to fly but a few moments before the vehicle would have to land and wait a few more years to make more fuel.