A theory.

*awkward wave*

Before I even start I just want to make it clear that I KNOW this would not work, as much as I would like it to. This requires that people are nice, and people are not nice. At 17 I've experienced enough of the world to know that one thing people aren't is nice. They can be kind, but for the purpose of this explanation those two adjectives mean completely different things. Being kind is doing nice, often selfless things for people you love, people you like or even just people you know - though in this case you are probably not selfless, you are being kind to make an impression. Being NICE is being selflessly kind to a complete stranger without expecting anything in return (and I mean this in the literal sense, not the "aw you didn't have you, you shouldn't have.. I wasn't expecting.." shit). *these aren't the definitions of the words but I thought I'd borrow them to make the differentiation between two points.
Yeah, so people aren't nice. And for this to work they'd need to be.

Here we go..
Instead of having a currency, or anything that is exchanged for a value and something in return, people just do their jobs. They don't get paid. But they don't need money. People do things for each other because they can. For example a teacher will teach a class of children because it is their job, if that teacher then wants to buy and apple they will go to a shop and the grocer will give them an apple because it is their job, the farmer will grow the apples because it is his job. People will do things for others because they will KNOW that they to can go to a shop and buy and apple or send their children to be taught. The governments won't need money because if it is someone's job to build a new road (which would be government funded) they will, knowing that if they wanted to go to a pub and eat a meal they could because it is that landlords job to provide that. People would do things for the love of the job, not the money they get out of it because money doesn't exist and it is not needed. If money had never existed would it be missed?
This may destroy all sorts of accepted systems by which we live, like the class system, but it would illuminate poverty and people wouldn't starve to death or live on the streets.
It would work because people would be nice to each other because they know that niceness will be returned in some form.
But it wouldn't work, because people aren't nice.
Oh, and probably because some people would freak if royals had the same amount of status as a shop keeper.