ryand
There are whole manuals on this topic so you're not going to get a simple universal answer such as "greater than X hours there must be an extra 1 or 2 pilots" that applies to everybody. There are national rules and then there are individual Company/Union agreements, so one pilots answer, such as FLCH's or Mr Angry's, are correct, but only for their operation.
Broad answer is it depends on variables such as the time of day of departure, end time of previous duty, start time of next duty, time zone changes....As an example of the nuances, we can do UK to Florida with no extra pilot, and the (night) flight back can also be done with just two pilots if the slip in Florida contains 2 local nights. If the slip is reduced to 1 local night then we have to have 1 extra pilot, depite the Flight time being unchanged..