Typically depends on the amperage required by each fan.
DON'T exceed a total of one amp from all fans combined, as that will usually short out the fan header and kill it. And may potentially cause additional damage to the motherboard it is plugged into. Personally, I try to stay shy of .7 Amps from all fans combined though.
Usually this means a maximum of two to possibly three fans per header. And I've never exceeded this as my fans are 0.20-0.4 Amps per fan, and I've just never felt safe going with more than two fans. I have had my fans throttle though with two 0.30 Amp fans (0.60 Amps total) connected to the same channel on my fan controller though (and the connector started getting hot, so I moved those fans to separate channels).