How closely may an artificial satellite orbit Earth without decaying appreciably each orbit? Just what the title states.
An artificial satellite will orbit Earth with some defined angular momentum.
An aircraft,on the other hand, relies upon it's engines to provide continuous forward velocity & lift.
I understand the mass of the satellite, shape of the orbit may be a factor here. As also the factors mentioned in dmckee's comment below. To clarify, the intent here was indeed to determine atmospheric drag. Mike & Peter, I proffer my apologies. 
How closely may an artificial satellite orbit Earth without decaying appreciably each orbit? Is there a definite formula/formulae to determine this by direct substitution of values, or is each such calculation unique?
 A: About 200 kilometers is a good benchmark. Even complete satellites (as opposed to small, high-drag fragments) will de-orbit within days (i.e. ~100 orbits) from that height.
Since drag depends for a large part on pressure and pressure sharply drops at these heights, the most important height is the periapsis (lowest point in orbit). However, a satellite with a highly eccentric orbit will spend most of its time near its apoapsis, not periapsis. Therefore the orbital decay rate expressed in orbits changes a lot less than the decay rate over time.
A: I also interpret your question to be "how low can an orbit be without decaying appreciably".  My layman's guess is that we can take a hint from the typical altitude of both the shuttle and the International Space Station orbits, which are (were) in the range of 320 to 400 km.  Presumably if they orbited any lower, the more frequent engine "boosts" would be too costly in both fuel weight and the effect on the mission. I think some experiments and activities can only be performed during free fall, and not during acceleration.
A: Regarding the Corona program, wikipedia says

The first satellites in the program orbited at altitudes 100 miles (160 km) above the surface of the Earth, although later missions orbited even lower at 75 miles (121 km)).

and continues to say

Corona orbited in very low orbits to enhance resolution of its camera
  system. But at perigee (the lowest point in the orbit), Corona endured
  drag from the Earth's atmosphere. In time, this could cause its orbit
  to decay and force the satellite to re-enter the atmosphere
  prematurely.

If you're looking for a 'general' case, I imagine it would be a function of your mass per cross sectional area in the tangential direction.  In other words, a more massive object of the same size would experience the same amount of drag but the drag force would be less significant due to its greater momentum.  It also depends on what you mean by "decaying appreciably".  Are you looking for something to stay in orbit permanently?  Or for a few orbits?
