I heard it (sorry, I forget where) as typing the sync command three times (as in: S Y N C Return, wait for the prompt, repeat, repeat). I also read that the origin was a particular system where it would take a couple of seconds for the disk to finish flushing its buffers, even after it had told the operating system everything was fine. Typing the command twice more gave the disk enough time to settle. It seems that over the years, the purpose was forgotten, and the advice was abbreviated as sync; sync; sync which wouldn't have had the desired effect (since the disk had reported the “all clear”, the second and third syncs would complete instantly and the prompt would come back too early).
I have never heard of a system where multiple sync operations have any use, and I am highly skeptical any exist. I consider this an urban legend. On the other hand, I find it highly believable that there would be systems where you should wait a couple of seconds after sync'ing and before powering down.
Googling leads to a few independent concurring analyses, e.g. The Legend of sync. See also Is execution of sync(8) still required before shutting down linux?.