The Sages forbade folding an item of clothing on Shabbat because folding helps it maintain its shape, ensures that it sits right on the body, and prevents wrinkling. Therefore, when one folds clothes it looks like one is fixing a kli (see below ch. 15). Only if one has a new white garment that he can fold by himself, and he plans to wear it on Shabbat because he has no other appropriate clothing, he may fold it on Shabbat (Shabbat 113a). Based on this, some prohibit folding a talit after prayer services; since it will not be worn again that Shabbat, folding it constitutes preparing on Shabbat for the weekday. Additionally, if the talit is not new, one may not fold it because this act of folding is more significant than folding a new item (Ĥayei Adam 44:24). Some who are meticulous follow this position.
In contrast, according to a minority position in the Rishonim (Orĥot Ĥayim), the type of folding that the Sages prohibited no longer exists. In the past, a clothes press operated by two people would be used to make the folds in clothing permanent. This is why the Sages only permitted folding a new white talit when the act is done by only one person. However, the type of folding we do nowadays is not so significant, and it does not look like “fixing” anything. Therefore, one may fold a talit along its original creases after services. Moreover, this is not considered preparing on Shabbat for the weekday. Just as a couch may be arranged on Shabbat even if no one is planning to sit on it, because its disarray detracts from the honor of Shabbat, so too a talit may be folded in order to honor Shabbat. Furthermore, doing so honors the talit as well; as an item used to fulfill a mitzva, it should not be left in an unfolded mess. Some prominent Aĥaronim follow this position and maintain that a talit may be folded normally on Shabbat. (See Kaf Ha-ĥayim 302:32 in the name of Yafeh La-lev; AHS 302:12; Or Le-Tziyon 2:24:3.)
The middle position, which most poskim follow, is that a talit may be folded on Shabbat as long as it is not folded along the lines of the original creases. The prohibition of folding clothes on Shabbat applies only when they are folded according to set folds; as long as the folding does not follow the ironed-in folds exactly, it is not similar to the melakha of Metaken Maneh and is not prohibited. This is the halakha (SA 302:3; MB 302:18; Ben Ish Ĥai, Year 2, Vayeĥi 13; SSK 15:49; Yeĥaveh Da’at 2:40). It should be noted that in practice, today’s talitot are ironed in a way that makes them difficult to fold exactly as they were at the start. Therefore, one may fold his talit in the regular fashion after prayer services, since he is not folding on its ironed-in folds.
A hat that got misshapen may be reshaped or straightened out on Shabbat. This is because it is a very simple thing to do, and is not considered fixing a kli (SSK 15:50).
The poskim disagree whether one may fold paper into forms such as boats or airplanes, or to fold napkins into special shapes. One who is lenient has grounds for his leniency, and one who is stringent should be commended (as explained below in 15:7).