I don't have the specification, but wikipedia states a current of 1.5A per pin.
This is supported by a datasheet from Molex for a power connector where it states 1.5A at 15V DC maximum per pin.
An additional support is this question where someone, who actually has the specification, is mentioning the 1.5A as well.
Considering the spin-up currents of 3.5" HDDs this doesn't seem to be a far fetched requirement. (I measured around 10W additional power during spin-up)
Now you have three 3.3V, three 5V and three 12V lines, which means you could draw a total of 91.35W from a single SATA power connector, but I'd stay away from maximum specifications.