I've been using and overclocing computer components for about 10 years now. After about a week of "burn-in" (running prime95/memtest/etc), typically, most of the components I've used did not change - they worked just as good as on the first day as they did a year later.
Except for these instances:
AMD XP 2400+ cpu. When I first got it, it was only overnight prime95 stable overclocked at about 1.7v. After weeks of use, it was all of a sudden stable at 1.6v at the same overclocked speed.
AMD 64 venice cpu. When I first got it, it was only 100% stable at 2700mhz 1.55v. After weeks of use, it was stable at the same speeds at 1.475v.
TCCD ram - got this brand new ram hoping for ddr600(300mhz) (all testing done at 2.8v). Was dissapointed that it would only boot into windows as high as 270mhz (unstable).
For day 1, I have records of the ram giving an average of 136 errors in memtest test #5 at 270mhz 1t 2.5-4-4-10).
After a few days of heavy use at stock speeds/voltages, I tried again:
For day 3, It gave an average of 8 errors in memtest #5 at 270mhz (1t 2.5-4-4-10).
Several weeks later, the ram runs flawlessly at 270mhz+, and even boots into windows as high as 310mhz.
Just my experience

Maybe only brand new hardware that hasn't been tested extensively by the manufacturer does this. And burning-in to me means just a few days/weeks of normal use and prime95/etc - not excessive volts or running the component at un-stable speeds.
If overclocking, don't worry about burning-in the component. Just find your max stable overclock and stick with it. If you want to see if burning-in helped, try a higher speed or lower voltage after a couple of weeks and see what you get.