Does the orbit of the ISS decay? I don't know much about the ISS, but I heard some rumors. The rumor I heard was that there is a very, very tiny atmosphere at the ISS orbit.
Yes. The International Space Station is on average orbiting at an altitude of around 230 miles (370 km), but is currently roughly at an altitude of 260 miles (418 km) as it just completed an orbital reboost a few days ago (or maybe it was yesterday, my biorhythm is all messed up).
You can track the current position relative to the ground (ground track), altitude, velocity, and a few other ISS telemetry data live via various websites, for example this ISS Tracker. The ISS is without this orbital reboosting constantly losing velocity and with it altitude due to slight atmospheric drag, as there indeed is some atmospheric pressure at altitudes it orbits. These low orbital altitudes are also referred to as Low Earth Orbits, or LEO for short.
Atmospheric pressure in LEO is around 10-8 Pa (Pascals) or 1.45*10-12 psi (pounds per square inch), which is of course a few orders of magnitude smaller than the Earth's average sea level pressure at 101 kPa (kilopascals) or 14.7 psi, but still enough to cause some orbital decay due to atmospheric drag to the ISS that orbits at the average velocity of 4.791 miles/s (7.71 km/s). To compensate for this drop in orbital velocity, the ISS periodically has to reboost and regain velocity and orbital altitude.
For easier appreciation of different values of (atmospheric or otherwise) particle density pressure: Wikipedia on Orders of magnitude pressure values, expressed in Pascals.
Edit: Note that since assembly complete and retirement of the Space Shuttle fleet in 2011, ISS' average orbital altitude is a bit higher than the numbers I give above. For some plots of that, see How often does ISS require re-boosting to higher orbit? Its current altitude (semi-major axis) is roughly 401 km (400 x 402 km at perigee and apogee, respectively). For information on specific orbital reboosts, see ISS On-Orbit Status Report. Last one (as of writing this update on 07/21/2015) was completed on the night of 07/10/15 to correct ISS orbital phase for the upcoming Expedition 44 launch to the station on July 22, aboard Soyuz TMA-17M with the expedited four-orbit rendezvous. Next ISS reboosts are scheduled for August 7 and August 24, 2015.