A Lubavitch chasid wears his talis with the sides folded under, at the shoulders, bunching the side material under rather than over the material that lies on the shoulder (see an example). Why?
The last Chabad rebbe, Menachem Mendel Schneerson z'l, made a compromise between his rebbe, the previous rebbe Yosef Yitzchok Schneersohn z'l, who wore a regular Lubavitch talis and his father R' Levi Yitzchak Schneerson z'l, a kabalist, who wore an all-white talis (see page 30 of this pdf). By folding under, it appeared all white, according to the custom of his father, while still being a talis in the style of the previous rebbe. The custom then spread to the rest of Chabad.
Since I inspired the question, I get to post the first answer:
I was told it's because the wife of the Lubavitcher Rebbe did not like the way the decorative knots on the side edges looked (they look unfinished), and would cut them off of his tallis and put in a regular seam.
So he started folding the knots under so they would not be visible (i.e. would not look bad) and the other chassidim copied him.
In Tzitzit Halacha LeMa'aseh (Chapter 8, footnote 93), R' Gurary quotes Reshimot Devarim (Volume 2 page 100) from R' Chitrik, who says that the custom of the world is to fold the Tallit over, so that the edge of the tallit is on the outside. The custom of the Chabad Rabbeim is to fold it under. so the the edge of the Tallit is on the inside.
In Kobetz Ha'oros U'Beurim - Oholei Torah #534, page 30, Rabbi Avraham Holtzberg suggests that this was done in order to conceal the black stripes on the Tallit.
Rabbi Gurary questions this answer, since when it is folded this way the stripes are even more visible.
Either way, the answer seems to be that Chabad Chassidim started folding the Tallit this way because their Rebbe did it this way.