Some have said that burn in for electronics is more our ears becoming accustomed to the electronics rather than the other way around. I don't want to start another flame war about burn in but after the first few hours (some say minutes) there probably isn't much change in electronics. Tubes may be an exception here because they certainly do wear with time and eventually burn out so it's not unreasonable to expect their sound to change with time. The heat they put out also has an impact on other components. Back in the days before solid state, the materials used in electronics may have been more sensitive to the heat put out by tubes. The concept of burn-in of electronics developed way back then, and is probably true today for tubed devices.
Listeners do report what they describe as burn-in on many devices and there's no arguing that they hear what they hear. Apparently just like DACs, our hearing samples the sound and we analyze the samples, Each time we sample a piece of music we tend to sample different parts of the piece and each time we have longer listening sessions we collect a different set of samples from all the pieces of music. Thus in each session we hear different things and form different impressions but by the time 7 months has gone by we have sampled the whole range of most of what we listen to on that piece of equipment and we have become accommodated to, and familiar with, its sound so we don't notice the things that stood out at first. Really expert reviewers probably have the ability to focus enough to sample exactly the same elements every time, but it's hard even for them. Personally, I thought my X5 sounded awesome right out of the box and I like you have liked it more and more with time. I have used it as a DAC and it compares favorably with a few more expensive stand alone DACs. Maybe that says I am not a great listener. Or maybe it says that there are other weak links in my system that don't allow me to hear the differences between the DACs. Who knows? Who cares if the music makes you happy?
Speakers, cans and IEMs are another story. Being a moving mechanical device they do have to be "broken in"--that doesn't sound good does it? Mechanical exercise is required to loosen up and stretch all the elastic parts and wear is required to break-in all the moving parts. Every device is different but 100 hrs is a commonly accepted standard for electromechanical transducers.
There's some really interesting information about our perceptions, hearing, break-in and ABX testing, etc over on the Sound Science section of Head-fi. The whole thing is worth a read.
