In the US there is an 8-hour flight time (or duty?) limitation with 2 crewmembers. To allow longer flights, a third crewmember is needed. The pilots alternate rest periods to allow a duty time extension.
In the UK this isn't really an issue I think the 2-crew duty limitation is 13 hours or so... only the longer LHR-SFO/LAX flights need a relief pilot. Certainly the jumbo's off to the far east would have 3, maybe even 4 pilots where 2 would serve as a complete "cruise relief" crew?
Perhaps someone else can enlighten us further?