Wire gauge of 40 pin IDE cable
26 or 28 AWG for typical ribbon cables (like the one in the O.P. picture).  Ribbons with bigger wires (smaller AWG) are more of a specialty.  Here's a datasheet for your generic ribbon cable, which specifies the wire gauge (bottom of the page).

P.S.  Of course, if one wire in the ribbon can't carry enough current, you could use several in parallel.