Yes, of course.
Think of your family. Does your mother pay your father to cut the grass? Does your father pay your mother to have sex with him? Do you give your kids money to lay the table? Do the kids pay the mother to cook dinner or drive them to school? Do you pay your husband or wife to listen to you when you tell them of your day?
Sure, some parents give their kids money when they do household chores, but in most families people cooperate without payment.
Where I live, even villages work that way to some extent. When someone wants to build a house, everyone gets together to build it. And they don't count hours and expect an equal return. It is just what you do, because everyone understands that they are dependent on each other. You can see this generous cooperation everywhere in this world when a disaster strikes. Suddenly it does not matter that time and things usually cost money, and people can create "goods" (material to build a dam) and "services" (the manpower to build it) seemingly out of nowhere.
Many "primitive" tribes live on that principle all the time, where the whole community takes care of the whole community. They hunt together. They farm together. They build together.
And a whole nation or world can work that way, too.
Just think of our (industrial) society without money. Not possible, you say? You are wrong. Goods and services do not simply disappear, if you take away the money that we use to pay for them. Money is a circular thing. You work and produce things that others need to earn the money to buy the things you need. If you delete the money, you can still work to produce the things others need, and they can still work to produce what you need. All you have to do is to keep on doing what you do, and despite the money gone, nothing changes.
But, you say, people won't work, if they don't have to. But of course they have to. If they aren't stupid (and people in small communites easily realize this, indepentend of their individual intelligence), they see that if they want to eat, dress, and sleep under a roof, they will have to work for their food, clothing, and housing. If you don't want to die, you will have to work.
And people actually like to work, too! People are easily bored. So they will do things. And while a few might enjoy to just lie around and watch tv, most people need to do things that give their lives meaning. People like to work in the sense that they enjoy doing meaningful things. Many middle-aged men get a depression when they lose their jobs, it is one of the most common reasons for depression in that age group. And not because they don't have any money. They do. But simply, because their live has become meaningless. And why do retired people do all that unpaid, voluntary work? Because they want to work!
So basically, if you took away the money, maybe people would stop creating much of the superfluous garbage that we use to drive our economy (like a tv in every room of the house or new shoes although the old ones are still good), and some of the more unpleasant things would need a bit of reward (just cleaning your own toilet is not something that all of us enjoy doing unless our new girl-friend wants to visit), but basically we would certainly still want, need, and create everything that makes our live worth living (from food, to clothing, to housing, to entertainment).
The only real changs would be that we would no longer have rich people. Because there wouldn't be anything to hoard and withhold from others.
Yes, there would still be theft and war, because there would still be people who love to take from others. But that's what I said: basically, everything would remain the same.