In contrast to the Aruch Hashulchan brought in this answer (and be sure to read Josh's link for some solid background information), The Mishna Berura on Shulchan Aruch OC 302:3 forbids folding the tallit after the completion of prayer unless the conditions listed below are met. It appears (See M"B SK 14 and others) that he holds it is forbidden because of "Nireh K'Mitaken Mana" - It appears as if one is one is fixing something (I'm not quite sure how to translate the halachic definition of metaken). However, perhaps from SK 19 it is possible to say that the Mishna Berura is also worried about preparing on the Shabbat for the weekday.
Here are the conditions that allow folding along the original folds on Shabbat:
The folding must be done for Shabbat itself (even though the mitzvah of tzitzit applies the whole day, if one does not intend to wear the tallit again that day it is forbidden. If the person wears the tallit by Mincha it is permitted to fold it after Mussaf M"B SK 13)
Only one person must do the folding (and he cannot fold it on a bench or the like - M"B SK 14)
They must be new, unwashed garments (new, unwashed garments are stiffer and therefore do not fold as nicely, and are therefore not considered as "Mitaken" M"B SK 15) - [I don't know how long a tallit is considered new. I don't have a source right now, but somewhere in Chapter 302 this is discussed with regards to a hat, the same thing would probably apply]
They must be white (folding colored garments "fixes" them better - M"B SK 16) - [As I brought in this answer, a Tallit is considered white, even though it has black stripes. I don't know if the tallit would also be considered white when concerned about folding on Shabbat though].
This must be his only garment, i.e. he is folding it so it should be nice for later. (If he has other Shabbat garments the Rabbis did not permit him to fold this one. - M"B SK 17)
The Shulchan Aruch then points out, and agrees with, the Mordechai who says that it is permissible to fold it not according to its original folds without a problem. The Mishna Berurah says that the Acharonim agree that this is the Din, but points out that if one wants to be strict and not fold it at all, it is still better.