On hard sport routes it is common practice to leave your quickdraws in place to make working the route easier, meaning you don't have to replace them each time you visit the crag.
On some really hard or steep sport routes key quickdraws (or sometimes all quickdraws) are left in permanently as stripping them out is a very difficult task due to the steepness of the rock.
In this interesting video Ian and his friend confront a 'quickdraw thief' at the base of a route and explain the ethics to him.
In trad climbing it has been common that a piece of gear left or stuck in a route has been considered 'crag swag' and has often been kept by the lucky climber who manages to free it from the rock. But this tradition seems to be changing as internet lost and found forums and other communication methods make it easier for climbers to return found gear.
VIDEO: Quickdraw Thief!