Under the New World Economy, material needs were no longer the focus or driving force of many people, rather, it was self-improvement, self-enrichment and the betterment of all. This effectively eliminated social problems like hunger and poverty and, as a result, money was no longer used. Humans took great pride in this, describing themselves as having "grown out of their infancy." The Federation, however, continued to deal with other cultures which had money-based economies, using credits, trade or negotiation instead. (Star Trek IV: The Voyage Home, TNG: "The Neutral Zone", "The Price", "Time's Arrow, Part II", Star Trek: First Contact)
Some cultures like the Ferengi did not appreciate the Federation's economic system. As a consequence, and in accordance with their extreme capitalist mindset, Ferengi historical records on 21st century Earth describe Wall Street with reverence. (DS9: "In the Cards"; VOY: "11:59")
"I'm Human, I don't have any money."
"It's not my fault that your species decided to abandon currency-based economics in favor of some philosophy of self-enhancement."
"Hey, watch it. There's nothing wrong with our philosophy. We work to better ourselves and the rest of Humanity."
"What does that mean exactly?"
"It means... it means we don't need money!"