I have heard opposing arguments about whether or not Communism was intended to be an unreachable ideal, or a workable system. Has Marx ever commented, either in the communist manifesto or otherwise, on which one is true?
The main thrust of Das Capital is that Communism is not only a workable system, but an inevitable consequence of the flow of history, and of the instabilities inherent in the capitalist system, which would result in a series of crises ending with the radical overthrow of the system and establishment of communism. In later works he seems to think it possible that countries will reach the same state by gradual processes rather than violent revolution.
Its less clear whether he considered communism to be an ideal, or merely "better than what we have now". He doesn't consider a post communist world, which suggests that he considered communism to be a natural and stable system, and the one to which countries would evolve if history is allowed to take its course.
As best I can interpret Marx, it's a mistake to think of Marxism — referring to that ultimate form of political community — as a particular system, structure, or process. Marxism is any of a set of systems that might occur when all class distinctions are erased and the ideal of liberty is achieved. For Marx, the failure of capitalism is the same as the failure of socialism, or of feudalism, or of most any form of political economy: one group in a society takes control of the tools and resources necessary for material production and social sustenance, and uses that control to exploit other groups. For Marx, if we eliminate the notion of class — remove the possibility that one group might take hegemonic control over resources that the entire community needs, so that no one suffers any existential threats — then whatever form of government or economics the community chooses to implement will be intrinsically non-oppressive and non-exploitive.
In simplistic terms, Marx is pointing out that we cannot cow happy, secure, well-fed people into doing something they don't want to do. We can't coerce them into low-paying jobs out of fear they might not get any job at all; we can't convince them to work exhausting hours or in dangerous conditions; we have no economic stick to drive people forward, so the society as a whole has to lean towards the carrot. We end up having to treat everyone as people-just-like-us, with all the same kinds of needs and desires, and that creates the conditions for fairness and justice.
As to whether this is a practical ideal... This approach has been used fruitfully within monastic orders and faith communities across any number of religions, through most of human history: Christian communes, Buddhist monasteries, Orthodox Judaism, Quaker and Mennonite communities, certain Islamic sects, etc. It's clearly feasible within small, dedicated communities, and it's part of the Liberal ideology that informs most of the modern world, but it seems to be a far off state in the current large-scale political-economic environment. It smacks of an idealism that jaded cynics like myself tend to scoff at. This is why, I think, Marx focused so heavily on the labor-revolution model. For Marx, getting people to see that they are part of an exploited class — at least people within liberal societies, steeped in lIberal values — was the first necessary step in getting them to reject exploitation and demand their own place in society.
Marxism is considered a workable system, but people forget that in works like Critique of the Gotha Program and Das Kapital, Karl Marx considered reaching the final stage of communism to be a process. From capitalism, some form of lower stage communism/socialism would form (the dictatorship of the proletariat, Permanent Revolution, syndicalist worker's cooperative, etc.) to guide the common workers towards the final stage of communism & a stateless, moneyless society. As socialist thinker Philip Gasper puts it: "Marx and Engels never speculated on the detailed organization of a future socialist or communist society. The key task for them was building a movement to overthrow capitalism. If and when that movement was successful, it would be up to the members of the new society to decide democratically how it was to be organized, in the concrete historical circumstances in which they found themselves". So while communism was considered a workable system by Marx, true communism was supposed to be the end goal after capitalism was overthrown, some type of anti-capitalist state/cooperative/worker's union was formed as an alternative, and that successful revolution defeats capitalism to create a true communist community. As I stated in a previous answer, that was kind of the goal of many of the socialist revolutions we saw in the real world throughout the twentieth century: form a socialist state to compete with capitalism, defeat capitalism, then have the state erode away through a final revolution or natural human advancement in order to reach a clean, stateless communist society at the end of everything.
The best know quotation on this by Marx himself would be the — rather surprising for many — excerpt from The German Ideology:
Der Kommunismus ist für uns nicht ein Zustand, der hergestellt werden soll, ein Ideal, wonach die Wirklichkeit sich zu richten haben wird. Wir nennen Kommunismus die wirkliche Bewegung, welche den jetzigen Zustand aufhebt.
[Communism is for us not a state of affairs which is to be established, an ideal to which reality [will] have to adjust itself. We call communism the real movement which abolishes the present state of things. (— English translation)]
Big caveat: This book alone can be quote-mined for the term "communism" for – hm, quite a lot of instances? That's of course no wonder at all, given the centrality of the concept within his thought. But that also gives a firm warning not to use this one quote to explain 'Marx on communism as ideal or process' once and for all. Marx elaborates quite a lot over the concept over the years and neither Marxists nor other historians must fall for the 'myth of coherence' over one quote from 1846 to describe Marx' view on the subject matter in total.
I'll repeat the quote posted by @Tyler Mc
Marx and Engels never speculated on the detailed organization of a future socialist or communist society.
It's an important point because since Marx never proposed a complete system he had nothing to comment upon as the question asked. What is called Marxism most of the times refers to several different system proposed later by other philosophers or leaders often with conflicting opinion, so there is not a single framework anyone agrees upon.
Just to give an idea how much Marxism as it is understood deviated from the original ideas I can point out that in The Eighteenth Brumaire of Louis Bonaparte Marx spoke against the systems based on a strongly centralised bureaucratic machine. He knew them well because he had to do with the French and the German ones for a big part of his life.
Marx basically had a philosophy of history and saw various polities such as hunter gatherers, villages, city states, feudalism and industrial capitalism in a progressive line in light of this philosophy.
He took economics as his bedrock motor of change and its the various crises of economics that propelled the change from one kind of polity into another. He called the stage after capitalism, communism and it will be the crises of capitalism into the next stage.
In line with Hegel, he understood the progressive changes in these polities as furthering the emancipation of man. Steven Pinker, who is no communist but a psychologist has argued that on many indicators, human life has increasingly flourished. This is evidence for Marx's thesis.
Marx saw this progression as inevitable. So, yes, he did think communism was achievable. He did not lay out a programme how this might be achieved. When, gor the sake of argument, we consider feudalism lasted in Europe for a thousand years and suppose the next stage, because of increasingly rapid change, would last half that. Then we get a figure of around five hundred years for industrial capitalism. Given that the industrial revolution began in England roughly two hundred and fifty years ago, then we're merely half-way through this period and there's another two hundred and fifty years to go. These are obviously very rough and ready figures. But its really to give a sense of historical perspective to Marx's thesis.
This philosophy of history, which Marx took from Hegel in broad outline, is so identified with Marxism that Fukuyama, an American political scientist, wrote a book on the dissolution of the Soviet Union titled The End of History meaning the end of Marxism.
Personally, I think Marx is correct. I don't see it being 'utopian'. After all, had you told a medieval peasant that people will be able to fly, have fresh water, light at the flick of a switch, instant world-wide communication, he would only snort and say, "what do you take me for? A fool!?"
Communism was not invented by Marx. He just improved it. Marx was a materialist and all of his ideas were realistic. That's why Marx thought communism was reachable.
But there are a lot of complicated technologies needed for that. Look to the Star Trek series. It's reachable, but will take a long time.