The upper limit to reliable operation, physically speaking, is due to electromigration. Which apparently is in the 10^7 A/cm^2 range. Whereas most wires and traces are in the 10^3 A/cm^2 range. So, you have about an 80dB dynamic range between burning out traces due to overheating (in the 100us to 100s time scales), until peak currents (ESD and other surges?) even begin to affect the conductor physically.
Current density isn't really a thing, when it comes to heating, but you can determine an upper limit.
Suppose the board is covered in a uniform layer of copper, which is carrying a uniform current. The copper plating has known resistance, and the board has a certain dissipation factor (typically around 8.3mW / (in^2 K)) due to convection on the surface (top and bottom, separately), and you define a fixed temperature rise for the board.
If you plug all these in, you get:
Missing variable: resistivity of copper ~ 17nOhm.m. Let's say 20, since it has some tempco and as-plated won't exactly be annealed either.
https://www.google.com/search?q=sqrt%281%2F%281+in+*+20+nanoohm+meter%29+*+%280.0083+watt%2Fin%5E2%2Fkelvin%29+*+20+kelvin%29+in+A%2Fcm%5E2For a 20C (= 20K) temp rise.
(I wrote this before, just rearranged for current density. Ref:
http://www.dutchforce.com/~eforum/index.php?showtopic=43392 )
If the thermal conductivity of the PCB is good (for FR-4, not really..), you can concentrate all the current on one side, but get dissipation from two sides; as a result, the current density limit goes up by up to 40%. It goes up further if there is a ratio of copper area to board area (i.e., you have a bunch of individual traces carrying current, separated by blank board area that's insulating around the traces but still able to dissipate heat). Although not by too much, because again -- limited by board conductivity. But if the board conductivity is good (say, an internal copper plane, spreading heat), it's even better still.
So current density for individual traces can be maybe 200-300% higher.
The IPC-2152 calculation (see
http://www.smps.us/pcb-calculator.html ) takes these factors into account. The two-sided PCB case is very close to the above figures (yay for consistency!), which is consistent with the old IPC-2221 figure. The values for internal planes and stuff are better still.
Tim