Just this November 2003, scientists at a meeting of the Geologic Society of America discussed the possibility of volcanoes erupting on Mars even today! Many pieces of evidence suggest that there was (or is) volcanic activity on Mars. First, the topography (the shape of the land surface) of Mars looks a lot like the topography of volcanically active areas on Earth. For example, there are cone-shaped land-forms (the volcanoes) and huge, flat deposits around them that look just like the lava flows that occur around volcanoes on Earth. Scientist have also identified basalt on Mars. Basalt is a type of rock that forms from lava.

Not in our human observation, because Mars is a "dead" planet. These volcanoes are possibly 1-2 billion years old, and the most recent lava flows are between 20 and 200 Million years old. So, it clearly erupted - but quite long ago.

Mars is smaller than Earth, and has therefore cooled more rapidly. It also had a smaller volume of radioactive material in its crust than Earth (because of its small size) and thus has used up this heat source.

At present we believe that the crust of Mars is static - because the planet is cool; it does not have plate tectonics like Earth, with active plates moving over the surface.

Reference:
martian volcanoes.

The answer is yes, but it hasn't erupted for a very long time (10 million years or so).