There is an obligation for us to give financial assistance to those in need. We should give those among us the aid they need to get by, even if it means that we end up giving to the same people repeatedly. One way to do this is to give to a fund that distributes money collected among the needy; the use of an intermediary keeps the recipients from being embarrassed in front of the donors.
Charity doesn't only apply to paupers. If a rich man is stranded out of town without access to his funds, it's tzedaka to help him, too, even though he may have coffers of gold at home. The Torah obligates us to help all those who are in need to the extent that we are able.
If a needy person is too proud to accept charity, we should try to persuade him to take it by calling it a loan (even though we never intend to collect). If someone has funds that they prefer not to spend, we need not assist them. We are only obligated to give others what they need, not to make them rich by paying their bills while they save their money. (See Talmud Kesubos 67b.) Even one who lives on charity must pay a portion of it forward to those who are needier still than he (Talmud Gittin 7b).
The reason to give charity is as we have stated: God wants us to help one another because it makes us better people and deserving of His kindness.
This mitzvah applies in all times and places. It is discussed in the Talmud in tractate Baba Basra (9a-10b) and in Kesubos (50a). It is codified in the Shulchan Aruch in Yoreh Deah 247. This mitzvah is #195 of the 248 positive mitzvos in the Rambam’s Sefer HaMitzvos and #38 of the 77 positive mitzvos that can be fulfilled today as listed in the Sefer HaMitzvos HaKatzar of the Chofetz Chaim.