With older TVs and some plasmas you can get phosphor burn where the static parts of the screen (like a game's HUD) stay on and "burn in" to the screen.
LCDs don't have this problem and nor should LED displays.
If you're talking about the effect of trails on fast moving parts of the screen then that's down to the screen not being able to update itself fast enough (i.e. response time) and that's not restricted to a PS3, but it won't do any damage.
^^ Actually, if the Pixel Refresh Rate is below a certain threashold for a certain refresh rate (16ms for 60 Hz), you can get a situation where the screen refreshes faster then the pixels can change state.
As a general rule, 8ms or better is fine for 60Hz displays.