It depends on many factors: the ambient temperature, maximum temperate rating of the cable insulation, the resistance of the conductor and the ability of the cable to dissipate heat, which depends on whether it's is buried, sheathed, in free air, coiled up and the how good a thermal insulator the electrical insulation is.
Here's a table giving general values.
http://wiki.xtronics.com/index.php/Wire-Gauge_Ampacity
Use the Wikipedia table, if you need to convert to metric.
http://en.wikipedia.org/wiki/American_wire_gauge#Table_of_AWG_wire_sizes
For 400mA I wouldn't worry about it, if it's thinner than #30, it probably won't be mechanically strong enough for what you need.