I do not believe that cables can be burned in. I do believe that speakers can be burned in, as the material that speakers are made from loosens up over time, as do the gaskets surrounding them.
I'm still undecided on electronics. Burn in (to me, anyway) for electronics is about thermal expansion causing problems with poorly seated components, or discovering if a part is going to die within the first 2 or 3 hundred hours. Good companies will do this burn in before ever shipping you a unit. Burn in improving sound for electronics, however, strikes me as a bit weird. Wouldn't that imply that any changes in sound quality were due to components leaving their original specifications, due to wear or damage?
On the other hand, I can very easily hear a difference with my solid state integrated amplifier between a cold start and how it sounds after warming up. Hence why I am still undecided on electronics.