Ribbon Cable Wattage
The maximum voltage is defined by the insulation on the wire, not the gauge of the wire.  It is the voltage (worst case) that the insulation can break down.  The maximum voltage, as well as the maximum temperature, should be printed on the cable.



The maximum current is defined by the cross-sectional area of the cable (AWG number).

The table I usually use is the one from PowerStream: http://www.powerstream.com/Wire_Size.htm

That table gives different current ratings for power cabling (long runs) and for "chassis" wiring (short wires between components or boards in a system). It also details the resistance of the wire, which is very very useful.

There are no exact precise values, only ballpark "rule of thumb" values.  The actual value for your specific wire would only be within a range since it'll never be an exact area all the way along.  The current rating is also dependent on the ambient temperature, and to some extent the type of insulation (some can handle the wires getting hotter than others). Often a more important factor is the resistance of the wire which, on longer runs and at higher currents, can cause unacceptable voltage drops.

The current, passing through the resistance of the wire, causes heating (\$P=I^2R\$) of the wire itself, and too much current will cause the wire to melt and "fuse".  This may go hand in hand with the insulation melting, but not always.

There is no "wattage" for a cable, only limits of the voltage and current.  I guess you could say the maximum wattage is the product of the maximum of the two, but that would be a misnomer, since you could be under the "maximum wattage" of the cable but have too much current, or too much voltage.  The wattage of a cable only makes any sense when you are thinking about the amount of power dissipated over a specific length of the cable, which is a function of the current and the resistance.  Remember - your "working" voltage isn't the voltage that is across the length of cable - that voltage is the voltage drop caused by the current flowing through the resistance (\$V=R \times I\$).

"Ampacity" is an Americanisationalism and could be construed as a portmanteau of Amp-Capacity. Most normal people use Amperage.