All the planets from Venus to Neptune have wind, not to mention Titan, Triton and Pluto. There are only two necessary conditions: an atmosphere and a pressure difference between two locations. (Weather reports will talk about high and low pressure systems, yes? The stronger the pressure difference between high and low zones, the faster the wind moves.) Life is not a requirement. In the case of Earth and Mars, pressure differences are created daily by solar heating, so both pre-conditions are easily met.

I'm not entirely sure what you mean by "sustainable atmosphere", but Mars has more than enough to create some very - very - familiar phenomena.

It's not a matter of the absolute pressure/mass of a planet's atmosphere, it's the relative difference in pressure between two locations. The air molecules generally don't care how many other air molecules surround them - they care about moving from more pressure to less pressure. If by "sustainable" you mean "permanent", then Mars qualifies (although Pluto may not). If the air was so affected by the mass of the entire atmosphere, then Earth itself could barely be considered to have winds at all - the speed and motion you see in the atmospheres of Jupiter and Saturn make Earth hurricanes look like a light breeze by comparison.

EDITED to deal with Reddit's lousy formatting.