The basic halacha assumes that once someone commits to give a certain sum of money to a certain tzedaka then that commitment is binding even though he did not actually say anything out loud – a mental commitment is considered tantamount to a vow (a neder) that one is obligated to fulfill. There is a claim that Sefardim are not required to follow this strict interpretation of the halacha since the Shulchan Aruch actually spells out explicitly that one must actually say out loud his commitment in order to be bound by it.
In Choshen Mishpat (212:8) the Shulchan Aruch mentions two opinions on this matter, and concludes that as far as tzedaka is concerned one must say it out loud in order for a commitment to be binding, which certainly implies that the basic halacha for Sefardim is in fact that one has not violated a vow if he made a mere mental commitment to give to tzedaka and then did not fulfill it. However, when the Rtiva (Shevuot 26b, mishum) mentions this opinion he adds that a person with fear of heaven should nevertheless still fulfill his commitment.
There are several possible practical ramifications of this requirement to fulfill mental commitments to give to tzedaka:
1) If a person sent a cheque to a tzedaka organization and it came back to the sender (eg. if the address was wrong), is it considered a vow to give to them? On one hand he probably did not say out loud, “I am committing to give this money to this charity.” On the other hand, the halacha considers writing equivalent to speaking, and he certainly wrote his commitment in the cheque itself. Some rule that it is indeed considered as if he said a vow, and others rule that in this instance we would not apply the rule that writing is like speaking, and hence it would not be considered a vow.
2) If a person gave money to another who would convey it the tzedaka recipient, and the middle-man subsequently refused to pass it on, would that be considered a commitment? The Chazon Ish ruled that in fact the one who gave the money was still required to give that amount to the tzedaka recipient, because of the mental commitment he had made. (As mentioned above, the basic halacha would not require a Sefardi to do so.)
3) It is common that a person commits to give tzedaka to a certain poor person, but then cannot find him to actually give it to him. In such a case the general solution according to most Poskim is to give that money to a different poor person, although Rav Elyashiv ruled that he does not have to give it to tzedaka at all since he had committed to give it specifically to that poor person.