Woah woah woah, loaded question alert. "Socialism" is a highly subjective word, with dozens of conflicting definitions. In fact, the definition of socialism has often been the subject of vicious arguments; in certain far-left circles, questions like 'was Stalin a socialist?' can lead to a debate that goes down in flames quicker than an Israel vs. Palestine discussion.

"Successful" is an even more subjective term. Successful at what?

In short, I don't think this is the kind of question /r/askhistorians can help you with. That being said, some examples you might want to look into are the Paris Commune (1871), the "Free Territory" in the Ukraine (1918-'21) and revolutionary Catalonia (1936-'37). All of those are frequently held up as evidence that 'see, it is possible to have a society based on workers' control and still maintain political freedom and a functioning economy' – though it's worth noting that all these experiments quickly collapsed because of outside pressure before they could prove or disprove much.

First, it would behoove you to be more specific about what you mean by "successful". What are some societies you think have been successful, so that we might use that criteria to compare?

For example, The Diggers come to mind (the radical protestant movement, not the SF hippies). A group founded in the midst of the English Civil War in the mid-17th century, their ideas generally reflect socialist beliefs - shared property, communal living, etc. Their success was that they did set up such a community which, by what little information we have to go on, seemed to work pretty well by most standards.

Except of course the fact that they didn't pay any taxes and they were religious radicals, therefore their presence threatened local leaders. These local magistrates conspired with the army and/or armed mobs to forcibly remove and/or murder the Diggers. That was not so successful I suppose. I'd encourage you to read "The World Turned Upside Down" by Christopher Hill if you want to learn more about them. Fascinating group, them.

Then there are the anarcho-socialist collectives in Catalonia during the Spanish Civil War. These groups formed as free associations of craftsmen and farmers, rejected both the Marxist unionists and the government fascists who wanted to exert control over production in the region, and (again, what little evidence we have suggests) they managed to increase production while sharing the fruits of their labor more equitably.

Like the Diggers, were also crushed by government forces, with the help of the Marxists who were threatened by their institutionless nature. Loads has been written about this movement, although many of the english-language sources are disappointingly shallow (I don't speak Spanish or Basque so I can't speak for those). Chomsky's got a good overview of it in a few chapters of his book "On Anarchism".

On a larger point, thousands of "societies" have sprung up throughout history in which the means of production are all controlled equally by members within that society. A family in rural Cambodia that pools income in order to purchase farming equipment is a "socialist society", as is a commune in northern Oregon in which members all work and share their goods and services. Socialism exists every day in the world around you, even though it is not the legally binding method of economic organization promoted by a nation-state. It's important to not conflate the idea of a socialist society and a government that officially recognizes socialism as its national economic model. The former does not require the latter, and the latter often does not bring about the former.