Bifurcation can be triggered in three ways: when the number of red tokens on the District line is at least three more than the number of blue ones on the Central line, if Beck's is multiplied by exactly 2.6, or optionally if the two stations are the same colour. Bifurcation is worth considering if you want to add confusion to the game or destroy an opponent's plans.
Tri-, quadri- and greater furcations have been known. As, indeed, have semifurcations - where only half a station name is played in one or more strands (a typical such move could be: Totteridge / Wealdstone). Even rarer are other fractional furcations. The record number of furcations known in any one game is 18, and the record number of strands open at the moment of victory is eight: both records were set in one game under the "Reykjavik '92" ruleset - a variant ruleset which is not only notoriously lax about the conditions under which bi-or-other-furcations can occur, but is one of only two rulesets to allow both a nullifurcation (zero active strands) and a non-integer fractional furcation, where the station fractions do not add up to a whole number of stations.
(Not surprisingly, the Boardman's Combined Stations ruleset owes a lot to Reykjavik '92, on the rare occasions that Boardmans is actually taken seriously.)