Would two planes passing each other at 1/2 the speed of sound create a sonic boom? Scenario:
Two fighter jets at an airshow are flying towards each other at 1/2 the speed of sound. (Their paths are offset so they will not crash.) When the pass each other, will either pilot or a spectator on the ground hear a sonic boom?
 A: No. 
To create a sonic boom, a plane needs to be travelling at greater than the speed of sound in the medium the sound travels in, namely the air.  Speed relative to other planes or relative to the ground doesn't matter.  Only speed relative to the air that it is moving through. 
A: At the interface between a solid and a fluid often the no-slip condition applies. In simple words it means that the molecules of air that are most close to the wing, have the same velocity as the wing. So if the wings of the two planes come close enough (depending on their relative velocities but probably much closer that practical) you could have air molecules which have relative velocities above the speed of sound.
I would love to know more about the dynamics of the fluid in such conditions, but I would expect it to be pretty much in the trans/ultra-sonic regime, adding some extra velocity from the turbulence, it is possible for a shock-wave to be generated and eventually propagate up to your hears.
As a variation consider two cylindrical plates initially in contact and at rest, that get separated with relative velocity larger than the speed of sound (but absolute velocity relative to the air that surrounds them below the speed of sound). A region of vacuum will develop between the plates. Air will then be accelerated up to the speed of sound to fill the vacuum, and after a while the air streams coming from different directions will collide with relative velocity larger than the speed of sound, creating a shock-wave. Pretty cool!
