In the original Battlestar Galactica, battlestars and base ships showed no damage after many hits (because they didn't have spare models to damage), until they exploded. Particularly obvious was a combination of this with overused stock footage. A scene filmed for one episode showed missiles striking a base ship, causing a rapid chain reaction of explosions and then causing the ship to explode. It happened so fast that the explosions didn't have time to fade away, which would have shown that they didn't actually blow up a model. Still, it looked convincing enough... until they reused the footage in another episode. This was their only shot of a missile hit on a base ship. But this time, they had to show a ship hit and not destroyed. So they used the hit shot - and cut away before the final explosion. And, of course, the next shot with the base ship showed no damage.
Extremely averted in the reimagined series. The Galactica looks as beat up as you would think, and grows worse and worse as the series goes on.
Also seen in the Star Trek: The Original Series and TNG. The show's budget wasn't high enough to damage and repair the ship models for episodes so we occasionally saw things like the Borg tearing up the Enterprise with cutting beams in an episode, and there would be nary a scratch on the ship after the battle.
Averted with later series. An entire episode of Star Trek: Enterprise is devoted to damage sustained from flying into a Romulan minefield in the previous episode. Also, when the ship takes damage fighting the Xindi in season 3, the damage remains in place until the ship returns to Earth and can be repaired.
Used rather egregiously in Star Trek: Voyager. With the exception of the "Year of Hell" two-parter, any damage Voyager ever sustains is repaired by the next episode, even though they're stuck tens of thousands of light-years from any shipyard capable of handling a Federation capital ship (see also Infinite Supplies). And they didn't have the "no budget to damage the models" excuse either, since the series used CGI.
Egregiously doesn't come close to how TNG handled radiation exposure. While the Enterprise [crew] was subject to radiation, T-1 second and no effects whatsoever (not even a mention to show up to sickbay). T+1 second of exposure and presumably everybody was dead. Oddly enough, Star Trek II (Wrath of Khan) was mentioned in one of this editor's physics textbooks as "a fairly accurate portrayal of death by extreme radiation".
The way angels and demons in Supernatural die is an interesting example. They can be nicked, sliced, and tortured using their respective magic knives for seemingly forever until they get stabbed once with it in the heart or gut and then they die rather spectacularly. One is left to wonder what property it is exactly of the knife that's doing the killing. Lots of monsters on the show work the same way, able to take a seemingly unlimited amount of damage from whatever weapon it is that is supposed to kill them until you stab them in the right place and then they die all at once.