
I believe not, it's simply to complex to function without money. People are gready and almost always want anything in return. There are cultures that build relations without money or goods, however they are far from modern.
I'm unsure whether you phrase this question in a technological context (e.g. cashless society) or a more common sense context (e.g. alternatives to using money).
We need some form of a medium of exchange in order to be able to interact, trade and to some extent be able to communicate. Money is essentially based on faith alone, if we lose faith in the intrinsic value of money then the whole system could collapse.
Now, in terms of a technological context, you can now pay for things on your smartphone, credit cards take away some of the need to carry insurmountable bundles of cash in your wallet and Money is being substituted in the socially-conscious world for things like deeds and other activities. Sort of like bartering for the modern world. I'd like to see it happen, if only out of curiousity.