Some designers use the copper traces as low valued resistors...for instance to measure a current.
Although esentially free, the problem with this approach is twofold:
1) The initial tolerance, since it depends how accurately the board manufacturer controls the etching
2) Worse still, the temperature drift. Copper has a HUGE temperature coefficient, about +3.9% each 10C. Since the current will produce self heating, plus the heating from other components make this approach very low precision, unless temperature compensation is applied.
I've also seen traces like this used as fuses of last resort. In other words, if an overcurrent condition occurs, the trace will burn up and prevent a fire. The problem here is the lack of precision....same as 1) above. Additionally the board is rendered useless.