About burning in speakers, all that I have are these measurments, that show a significant change in measurable characteristics over 72 hours of burn-in :Burn in - Hydrogenaudio Forums
However, someone argued that after several days of rest, the characteristics should go back to their initial values.
And a survey made by Matrix-hifi among speakers manufacturers :Matrix-Hifi
(Go to "El Rincon", 09/02/2006: Rodaje de altavoces: Lo que opinan los fabricantes )
We can see that among 21 speaker manufacturers, one third has no opinion (they often say that "according to their customers" etc) , one third say that speaker burn-in is made nearly instantly (it takes no more than several seconds), and one third say that it takes more than one day.
...and one who said that burn-in was a bad thing because it shortens the lifespan of the speaker (JBL).
I don't know of any evidence of burn-in regarding sonic performances of hifi electronics (except listening accounts).
The case of CPU burn-in used by overclockers is sometimes cited as a proof that semiconductors have a burn-in period. Actually, CPU burn-in is a urban legend. Measurments show that burning in processors actually decrease their overclocking ability, not the opposite (see for example AnandTech