Star Trek
In "Silicon Avatar" we see Enterprise at warp. Sensors detected disturbance on Melana 4, which is 27 hours away at their current speed, which is warp, but below warp 8. So minimum sensors range is 27 light hours or 2.916 x 10e10 kilometers.
In "The Wounded" we have Enterprise searching for Nebula-class starship that was on silent running and probably used some measures to hide itself. Enterprise scanns radius of 10 light years, but we don't know from which range they detected Phoenix.
Voyager episode "The Raven" gives us sensors range of y light years when searching for Borg ship.
TNG episode "The Chase" states that Federation long-range sensors cannot detect limited-scale life on planet; however, they can detect state of oceans on planet.
Star Wars
From ANH novelization we know that ships in hyperspace cannot be tracked accurately, but their vector apparently can be roughly determined (TESB novelization). Imperial Star Destroyer was unable to detect Millenium Falcon sitting on back of their command tower, and had trouble tracking ships above or below horizontal plane, suggesting 2D radar-type sensors mounted in globes.
(unfinished)
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