Mars, which has a tiny atmosphere that has more than 100 times less pressure than that of Earth, is yet to be visited by such a probe. The Soviet/Russian program was scrapped in the 90's due to financial reasons. NASA/JPL also had some experiments in the 90's, but there's no such a real mission expected anytime soon.
However, a private group of space enthusiast, the Mars Society of Germany has proposed ARCHIMEDES, a short duration, low cost Mars balloon project, that would be launched as a piggy-back payload on AMSAT's P5-A orbiter. (About AMSAT P5A in german) Archimedes was named after the greek philosopher who discovered the floatation principle.
After considering other options, namely balloon deployment in air and balloon deployment after touchdown on the surface, it has been decided that the balloon would be deployed in space, its drag slowing down the probe to slowly sink to its operational altitude. This way, the ARCHIMEDES mission will demonstrate the technology for inflatable atmospheric drag devices on Mars. (This part of the design is novel.) This means it will provide valuable data even if later phases of the mission fail. By the way, the nominal duration of the mission is 10 sols (Martian days).
Apart from testing the technology and gathering data about airflow during entry, there will be three scientific experiments onboard.
A camera, provided by DLR (the German space agency), which will be based on the ROLIS camera on the lander of the Rosetta space probe. It will be able to achieve a resolution of up to 20 cm per pixel at a 7 km distance from the surface. While this resolution is not really stunning - HiRISE on the Mars Reconnaissance Orbiter almost reaches this at its highest resolution -, it will be able to take images from an oblique, 45 degree perspective.
A magnetometer, provided by the Technical University of Braunschweig. Measurements of Mars residual crustal magnetic field were last made by the Mars Global Surveyor space craft during the aerobreaking phase of the mission, in an altitude range between 100 km and 200 km. Archimedes would be able to make more local measurements. The combination of a high resolution camera and a magnetometer makes it possible to correlate magnetism and geological features. It would also be the first magnetic measurement below the ionosphere. It could also be compared to magnetic field measurements at the same time on board the orbiter.
Atmospheric sensors (thermometer, barometer, hygrometer), by the Finnish Meteorological Institute (FMI).
Due to weight and power supply constraints, the communication will be low power (few Watts), targeting the orbiter.
A series of experiments have already been carried out.
Regina - Residual Gas Inflation test for Archimedes. Its objective was to test balloon deployment in the vacuum of space and zero gravity, at about 100 km above Earth. Secondary objectives was testing onboard subsystems, computers & telemetry. Regina was launched from the Esrange in Kiruna, northern Sweden, as part of the Rexus-3, rocket for student experiments. All experiments went perfect except for one glitch: 160ms after the motor separation the payload hit the Regina module. The collision resulted in a tumbling motion of both, and Regina drifted away, leaving the field of view of the camera on the other module.
Regina was considered lost, as there were no funds for a complicated recovery effort in the far north environment. However, residents found the module and returned it to the Launch Center. The computer was recovered in such a good state that it will be used in the next experiment. After long and careful analysis of the data in the recovered module, taking months, it was decided that the experiment was successful, and the release and inflation of the balloon had gone as planned.
More images about Regina here
Next phase is going to be MIRIAM - a balloon probe that is a 1:2.5 scaled complete model of Archimedes. It will be launched in March 2008 from Sweden, to an altitude of 200 km.
If all goes well, launch of Archimedes to Mars can probably be expected to happen in the 2011 launch opportunity.
More about the Archimedes project at The Mars Society and The Mars Society, UK.