The Ben Ish Hai (Rav Yosef Haim of Baghdad, 1933-1909), in Parashat Ki-Teseh, discusses the parameters of the prohibition of stealing (listen to audio recording for precise citation). He writes that the Torah forbids stealing any amount of property from anybody – Jew or gentile, adult or child. The Ben Ish Hai emphasizes that it is forbidden to steal even from a non-Jew who has been hostile toward Jews. In fact, he adds, stealing from a non-Jew is a more grievous offense than stealing from a Jew. For one thing, he explains, it is less likely that a gentile victim will forgive a Jewish thief for his crime than a Jewish victim would. Therefore, one who steals from a gentile has virtually no chance of achieving full atonement, which requires the victim’s forgiveness. Secondly, stealing from gentiles empowers the "Sar" – the heavenly angel supervising the gentile nations – to steal from the bounty assigned to the Jewish people. This crime is punished measure for measure, and the blessings assigned to us are instead diverted to the gentile nations.

Money amounting to less than a "Peruta" does not have the formal Halachic status as money. For example, 3-4 pennies would not be considered "money" in the strict Halachic sense of the term. Nevertheless, the Ben Ish Hai writes, it is forbidden to steal even these small amounts of money, because of the Halachic principle of "Hasi Shiur Asur Min Ha’Torah" – even "half-amounts" of prohibited activity is forbidden. However, it is permissible to take an object that has very little value if it can be reasonably assumed that the owner would allow taking that object. The Ben Ish Hai gives the example of a twig of straw. If a person passes by somebody’s pile of straw, he may take a single twig if he needs it for some purpose, since the twig’s value is less than a "Peruta" and it can be reasonably assumed that the owner would not mind. This does not apply, however, to taking a small piece of straw or another item that is part of a utensil or some object of value. The Ben Ish Hai discusses the case of hand-held fans, and rules that it is forbidden to take a small chip from the fan. Even though the chip in itself is not something that people ordinarily care about, it may not be taken since it is part of the fan and its removal could damage the fan. The Ben Ish Hai makes an exception in the case of an old, dysfunctional fan, which the owner presumably does not care about, and from which one may take a small piece of wood.

This entire discussion applies only on the level of strict Halacha. But on the level of Midat Hasidut (an additional measure of piety), the Ben Ish Hai writes, one should avoid taking anything that does not belong to him, regardless of the value and even if the owner can be assumed not to mind.

The Ben Ish Hai writes in this context that special care must be taken with regard to the property of the synagogue. One who borrows a Siddur from the synagogue must ensure to return it, and the same applies, of course, to anything belonging to the synagogue.

It was customary in Baghdad for people to remove their shoes when entering the synagogue. The Ben Ish Hai discusses the case of a person who, as he leaves the synagogue, notices that somebody had taken his shoes, and left behind a different pair. May the person take the pair of shoes that had been left? The Ben Ish Hai writes that if the person who took the shoes left behind a lower quality pair, then one may take that pair of shoes. However, if the person left behind a pair of shoes of equal quality, or of higher quality, than the shoes he took, then we must assume that this was an innocent mistake, and it is therefore forbidden to take the shoes. One must leave them in the synagogue until the owner comes to retrieve them. The modern-day application of this Halacha would be the case of somebody who took somebody else’s coat and left behind his coat.

Summary: It is forbidden to steal any amount of money or property from any person – Jew or gentile, adult or child. Strictly speaking, one may take without permission an object that has very little value if it can be assumed that the owner would not mind – such as a small chip of wood or straw – though it is preferable to avoid taking even such items. One must exercise care with regard to the property of the synagogue, and ensure to return any Siddur or other object belonging to the synagogue that one borrows. If a person notices as he leaves the synagogue that somebody took his coat and left behind his coat, he may not take the other person’s coat, unless its value is lower than that of his coat which the other person took.