For PvP, you may wish to save sprint mostly for chasing down your fleeing enemies, especially once you get [Blind] and [Vanish].
In PvE, sprint provides a very useful "get out of jail free" card.
Ostensibly a defensive ability, Sprint can also be used to return to the boss as quickly as possible, thereby maximizing time on boss and, in turn, DPS.
The Sprint functionality is identical to the effects of the [Swiftness Potion] created with the Alchemy skill, except the potion will break stealth.
Use Sprint to quickly close the distance on enemies that are trying to snare you or otherwise keep their distance. Especially useful against hunters and mages who've just blinked away.
Patch 9.0.1 (2020-10-13): Now learned at level 5 (was 26). Rank 2 now learned at level 31 (was 66). Running on water as Subtlety moved to Rank 3 and now learned at level 43 (was 61).
Patch 7.2.5 (2017-06-13): Sprint now allows Subtlety Rogues to run over water. This is only possible when running forward.
Patch 7.2.0 (2017-03-28): Rank 2 added at level 66: Cooldown reduced by 60 sec.
Patch 7.1.0 (2016-10-25): Cooldown increased to 2 min (was 1 min).
Patch 5.0.4 (2012-08-28): Now learned at level 26 (was 16).
Patch 4.0.1 (2010-10-12): Cooldown reduced to 1 min (was 3 min), duration reduced to 8 sec (was 15 sec), now learned at level 16 (was 10), and no longer learned in ranks of 50/60/70%.
Patch 3.0.2 (2008-10-14): Cooldown reduced to 3 min (was 5).
Patch 0.11 (2004-09-29): Can now be used while stealthed.