The only satellite I know of that was shaped to have low drag was GOCE, which orbited at 250 km.
Since it was vital to ensure that the measurements taken are of true gravity and not influenced by any movement of the satellite, this unique five-metre long arrow-shaped satellite had none of the moving parts often seen in other spacecraft. The satellite, together with its instrumentation, actually forms a single composite gravity-measuring device.
The satellite orbited Earth as low as possible to observe the strongest possible gravity-field signal – hence GOCE was designed to skim the edge of Earth's atmosphere at a height of about 250 km. Low fuel consumption meant that its altitude could be lowered to 235 km in 2012.
An electric ion thruster at the back of the satellite continuously generated tiny forces to compensate for any drag that GOCE experienced along its orbit.
The need to fly low and be ultra-stable led to a novel satellite design that minimised air drag and torque and excludes mechanical disturbances. The result was a slim 5 metre-long satellite with a cross sectional area of about 1m2, weighing in at about 1050 kg. The satellite was symmetrical about its horizontal plane and had two winglets that provided additional aerodynamic stability.
You can see this places constraints on the satellite's shape: you can't have protruding solar panels, antennas etc. This means it's only done when really necessary; for most purposes it's much cheaper to go to a slightly higher orbit instead.