It seems to me that in a Kardashev Type I or higher post-scarcity civilization it would be a two-tier "economy". Anything that can be auto-produced or replicated is essentially "free" save for the energy needed to produce the item, and the energy to produce the replicator etc.
I can sort of see how that would eliminate the need for currency, or even electronic fiat currencies. So when someone from the Federation boastfully says "We don't need/use money", I always took it as being unspoken that they really meant "We don't need/use money to LIVE."
However, there would always be a higher-tier economy, for items, systems, or services that cannot be directly replicated. Historical antiques of original provenance, or items of artistic merit come to mind. Personal services, such as hand-cooked meals by a famous chef, or even just a popular local restaurant, where food cooked over heat, cut by hand, from local "real" produce and meats would be another. Or industrial arts, where a certain designer's vision is more appreciated than the simple basic functionality an AI or an expert system may turn out.
Housing would be another. Everyone/anyone can get as many square meters as they might reasonably want for "free". However if you want a cabin on a lake, to be alone on a prairie, a certain view of the San Fransisco Starfleet HQ and the Academy grounds, it seems reasonable that you may have to trade or pay extra for that.
And people with skills, or unique abilities, they may care more about fame and appreciation than the money of this higher tier economy, a less altruistic but still non-material way of the old "we strive to better ourselves and humanity"-saw that got trotted out on the show. And we DO already have some parallels to this already, such as the massive amounts of time and effort that get poured into some internet/software/technological open-source projects. Instead of privatizing it, it's given away for free, just for the recognition, or the desire to "change the world" with whatever it is they've created. And if there is monetization of the work, it's a higher-tier solution, say someone like Linus Torvaldis, where they then consult, get speaking fees because of their fame, or write books or whatever...
Or look at the U.S. Military... What does some E-whatever in the Army or Marines get paid fighting or being overseas in AWOT, and compare that then to the six figures some hired-gun from Dyncorp gets? And it's an all-volunteer military, nobody's been drafted into it since 'Nam.
Although granted, the guy at Dyncorp would probably never get hired if he didn't have a successful combat arms stint in the .mil first...
So I always assumed that in the Federation, you didn't need any money to wake up in the morning in your home, turn on the lights, have the replicator make you coffee and scrambled eggs, but you still darn well did need money if you wanted an original Rembrandt painting, and a cabin in the woods to hang it in, with your own pond to fish and swim in, vs. some apartment in an mega-rise arcology with a community pool somewhere.
