American Wire Gauge, also known as Brown & Sharpe Wire Gauge, is a commonly used measurement of wire diameter, arranged in a geometric progression. Other popular wire gauges include the Imperial Standard Wire Gauge and the Birmingham Wire Gauge. AWG was designed to be used for non-ferrous wires only.

The nearest approximation I can get (mostly based on tables) is:

Wire Diam. in Inches = .324861" * (.98054)AWG
(.324861" is about 8.25147 mm, if you like metric better)
AWG values start with the largest wire, 0000000 or 7/0 (treat as -6 for above formula), at .6513" and get about 10.9% smaller as the AWG value increases.

Note that for stranded wire, the diameter will usually be slightly larger, depending on how the strands are arranged.
(see if you can find the large table at http://www.brimelectronics.com/AWGchart.HTM for more detail on that)

I'd like to thank Google, http://www.archers.org/gauge.htm, and the many wire gauge tables out there for their help in the creation of this write up.