This page provides the connector style and pinout for the Fan connector used on the ATX Motherboard.
The Header attached to the mother board is normally a male 3-pin header w/ locking tab.
However the 4-pin header is also some what common
The mating connector coming from the Fan cable uses Female sockets.

Not all fans or mother boards control or power the fan assemblies the same way.
In many cases the Fan will run one wire to the three pin header shown below [Sensor pin],
and also use an additional Molex connector to provide power to the fan [Male/Female or both].
The only fan header specified in the ATX standard [that I know of] was optional, and was a 6-pin connector.
Also, fans may be either 5 volt DC or 12 volt DC fans, the table below shows a 12 volt DC fan connection

All other ATX header pinouts, or
BTX motherboard header pinout.

The fan pin out below could also be called a SYSFAN, or System Fan.

The pin out table above provides both the connector pinouts and wire colors for the cable assembly.
I have also seen 3-wire cable assemblies running from the fan that used White, Red, Back. [5 volt system]
Pin 3 may also be called 'Rotation' instead of 'Sensor' both meaning the same thing [is the fan turning]. No data on copper AWG wire size is provided here.

PC Fan

Additional Mother Board form factors and processor types are listed on the OEM MotherBoard Manufacturers page. Memory Module formats and manufacturers are listed on the Memory Module Manufacturers page. A few computer manufacturers may use non-standard or proprietary components in their systems. Use this pin out tabel [signal assignments] for the fan header as a guide only. Many companies may use pinouts that differ from the pinout table above. First try to determine the pin out of the headers listed above from the material that shipped with the computer. Next review the ATX Motherboard specification.

Of course there are other possible fan pinouts;
The fan pin out shown below is the cpu Heat-sink fan on an ASUS P5N-E SLI Mother Board.
Although the cable only fits in the Molex one way [and still lock], the Black wire is ground.

The fan is powered by pins 3 and 4. Pin 2 is the speed sensor and pin 1 controls the fan speed [Pulse Width Modulation].
The ASUS Motherboard also has two other 3-wire fans. One fan in the front of the chassis and one on the rear panel.
Some Motherboards may also support a fan for the chipset, my old AV8 Mother board has an NB-Fan [North Bridge chip-set].
In many cases the Chip-set may use a Heat-pipe and not require a fan.
Of course there is also a fan attached to the power supply, which is built into the power supply.

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