Mike quotes the code (300.13B Device Removal) but misunderstands what it means. The paragraph's 1st sentence starts out, "In multiwire branch circuits,". That means where 2 or 3 circuits with 1 shared neutral wire are passing through a box. You'll probably never see this kind of wiring in a home, but if you have 2 or 3 circuits sharing a neutral in the same cable or raceway supplying several fixtures and/or devices, they want you to pigtail the neutrals (and only the neutrals!) at each device or fixture connection.
Otherwise, because it violates common sense (and cost more in T&M), pigtailing is not recommended. One connection is always better than two, and a wirenut connection is no better than the dual screw connections on a duplex receptacle (never put 2 hooked wires under one screw though). The other part of that is, if you can't fold 4 or 5 wires each 6 or more inches long connected to a duplex receptacle neatly into a normal size wallcase, you probably shouldn't be doing this kind work.
The simplest explaination of the wiring method this code refers to is where you have two 3-wire cables terminating in a box - 1 feeding in and 1 feeding out to the next box. That's 2 blacks, 2 reds, 2 whites and 2 grounds in the box. The feeding black wire is one circuit on a circuit breaker, the feeding red wire is another circuit on a different circuit breaker and the feeding white wire is the shared neutral for both circuits. When installing a fixture or receptacle at that box on either the red or black circuit, they want you to pigtail the neutral wires to prevent interrupting the other circuit during removal (replacement) of the fixture or device.
Like I said, this is not a wiring method that you're likely to find in a home.
And in the case of a GFCI receptacle, you can't use the load side of a GFCI to protect a downstream circuit with a shared neutral anyway, so you still pigtail the neutrals to abide by the code. However, if there's a downstream circuit from that GFCI that's a 2 wire (1 circuit) offshoot, than since for that portion of the circuit's neutral it's no longer being shared, it isn't required to be part of the pigtailing and you can connect the offshoot to the load side of the GFCI. And that could be anything from a receptacle right next to the GFCI in a 2-gang config or several more fixtures and/or devices.