I don't believe in a world were money doesn't exist, and seeing some statements below about communism, well yeah, if communism truly works, money would become obsolete, indeed. What is the point in money if everybody has as much as everybody else, eh? And that would be communism in the most extreme form (in which even Marx himself didn't believe, so I'm told).
The achillesheel in communism, and that's also the reason why it never existed, is that you need a strong leader who can reform a political and economical system with a firm grip, without much resistance, as huge changes must be set through. Something communism actually also forbids since power corrupts, which is the core sentence on which the entire ideology was based, and if we see how Stalin did... Well, weakness shown, and communism failed before it even came to be.
But what if communism did have the success Marx wanted to see? Also making money obsolete, allowing us to live without it... That sounds like an utopia in general to me, as that would be the end of loads of crime (what is the point to take risks if you don't benefit from it), no more poor (everybody has the same share after all), no more people corrupted by the power money gives... Yeah, that is what a world without money, and a world of TRUE communism would have to bring us... Utopias cannot exist, and if they can it's never for long. It's hard to predict how, but that perfect world will fall pretty soon, I'm afraid. Actually I'm sure of that. That's also why I do not believe in the economy depicted in Star Trek.
Capitalism is a failure, that much is true. Everybody saying otherwise, must do a reality check. A few group of people having more money than billions of others altogether, who can work their ass off hoping to get enough to pay the rent, IS a failure (but alas reality). But a world without money, or of true communism cannot work either.
Money came to be because trading stuff didn't always work. What if I can make stuff only a butcher needs. Then all I can be "paid" with would be meat. And sooner or later I could have more meat than I can ever eat in my life (not to mention, how can I prevent it'll rot). Money came to be to solve those kinds of issues.
I hate money, I really do. With all my heart. Loads of crimes and wars where fought over money. And money also brought us an economy where only a few can really profit. It did more harm than goo. But in the same time, it is essential to get economy working at all. Dang!