I would like to point out at this point that there's a BIG difference between running-in something like speakers, that actually have moving parts and the putative "burn-in" apparently required by some electronic equipment.
It shouldn't take too much imagination to realise that the movement of a speaker will, at the very least, cause the cone material to change stiffness with use, which will almost certainly affect the sound (whether that's noticable to the user probably depends on the speaker in question and the user).
It is also a fact that electronic components, especially ones that get hot in use experience a change in electrical characteristics with age (and in some cases with temperature, which is why some components will sound different when first switched on), so it's perhaps not unreasonable to expect something like the sound of an amplifier to change as it ages.
Then of course you've got something like a plasma TV whereby the phosphors on the screen need time to settle down to prevent screen burn, which is something that is clearly a real enough phenomenon, given that the manufacturers will advise the user to use a lower contrast/brightness for the first X hours.
The question as to whether manufacturers should run/burn in their products prior to release for sale is an interesting one though, I've got a vague recollection that some do this already or offer the option to do it, at the consumer's cost.