What exactly is breakdown voltage of air? Most of the online sources say that the breakdown voltage of air is 30kV/cm. I've made a Cockcroft Walton multiplier and I can see the air breaking in between 17-18kV/cm. Only in a discussion at one online forum : , someone claimed it to be 17kV/cm. 
What exactly is breakdown voltage of air at STP?
 A: It is correct that there is no such thing as a breakdown voltage, as stated earlier.  This becomes obvious since the units are given as V/m, which is represents Volts per meter, or Electric Field strength.
Also, unless one is measuring the field in between two plane parallel metallic plates, the Electric Field will, in general, not be uniform, I.e., the field strength (the amount of "pull" on an electron), will vary with position.  This shape does matter, and sharply pointed emitters can cause breakdown at values considerably less than the maximum measured in a uniform field.
The Volts/meter relationship is also pressure-dependent, and this relationship goes nonlinear at low pressures (not enough charge carriers) following Paschen's law.  It also varies with humidity and other contaminants, which usually increase arcing.
A: The 30kV/cm value refers to the electric field value.  Between clean parallel plates with nicely shaped edges, it might be possible to attain 3kV in 1mm. In real life, however, 10kV/cm is a much more reasonable design value if whatever you are building needs to reliably attain its design voltage. This is based on five decades designing and building HV ion sources and accelerators.
Previous comments also noted that the electric field is the controlling factor, and sharp points, roughness, and dust can increase the local field compared to smooth, clean, and large radii surfaces, and will breakdown the air around them regardless of how far they are from another electrode.
