In Islam there is a difference between voluntary charity and what I would call obligatory charity (as opposed to "forced"). Voluntary charity is either known as sadaqa (alms) or infaq fi sabilillah (spending in the service of Allah (swt)), whereas obligatory charity is zakat, the third of the five pillars. For most Muslims, the thought of not paying zakat is looked on with distaste because the voluntary nonpayment of zakat when one is obligated to and has the means to do so is tantamount to disbelief. Likewise, in the past, zakat was equivalent to a national tax, obligatory on all Muslim subjects of the realm, so the classical notion of zakat vs. modern income taxes is not that far off.
The thing is, Muslims were and are encouraged to pay both the obligatory and voluntary charities. It's not a question of suggesting that voluntary charity is good, obligatory charity is bad. Both are good. Paying zakat is not only for the benefit of the poor and others who are eligible to receive the money, it's actually as much for the benefit of the payer's soul. Zakat literally means "purification and growth" because the payment of zakat leads to both the purification and growth of one's soul. The act of giving zakat helps to dampen the soul's love and lust for material wealth. A hadith from Tirmidhi's collection has the Prophet Muhammad (pbuh) saying:
The trial for my ummah is wealth.
By paying zakat we both fulfill our obligation upon the rights of men (just as prayer fulfills our obligation upon the rights of Allah (swt)) and increase our concern for our fellow man.