Money of some kind will always be there as long as people enjoy exchange things, and assign values to the things they exchange.
Before the conception of money, people simply exchanged one thing for another. You can argue that the things they exchanged were money. If you use electronic payment to obtain physical goods, you are effectively exchanging information for something physical. However I think you would definitely agree that you definitely exchanged money. The point is that the money as a concept evolves over time.
I think there is a question that those people who propose moneyless society need to ask themselves. The question is whether they are willing to give away their favourite childhood toy away for free, or they want something back in exchange. The toy itself may not have any value in other people's opinion. However for the toy's owner, it may have some values because of the associated memories. I suppose this is why sometimes celebrities' possession can attract large amounts of money at auctions.
The money is only there to help the process of exchanging things. It can have many different forms. Ultimately I think as long as people need something to help them to exchange things, that thing will be called "money".