Well, it seems the first mistake people have made here is coming to a mutual agreement to what Communism actually is. I see most have taken the assumption that Communism refers to the history of Marxist-Leninist states of the 20th century - which considered themselves to be "building socialism."
To put it in plain terms, Marxist-Leninist theory (assuming we're talking about the policies of Stalin and later Mao) attempted to explain why revolutions had taken place in the under-developed, largely agrarian countries rather than the industrialized, advanced capitalist countries of the Western world - this mainly rests on the idea of the "weakest link of the chain" concept that Lenin elaborated on in Imperialism, Highest Stage of Capitalism. With the failure of the German Revolution of 1918 and the failure of the European working class to rise in revolution - only instead the forces of reaction had defeated it. The Bolsheviks were taken aback by this - how could the Russian revolution survive without the industrial support of a Bolshevik Germany? What followed next was the reintroduction of limited market economies in Lenin's NEP, and later Stalin's economic planning. Of course, there's a lot of debate among Marxists whether Stalin's "Socialism in One Country" was really a continuation of Lenin's thought, but the majority opinion in the 20th century, is that it was. Marxist-Leninists believed that it was possible to "build socialism" via the leadership of the revolutionary vanguard in pre or not fully developed capitalist societies - and then transition into communism - the final stage of human development according to Marx.
Mao took Marxism-Leninism to a more radical level, believing that the peasantry of an imperialized country could be a revolutionary class (in direct contradiction to what Marx thought) and directly build socialism, bypassing capitalism entirely.
During and since the collapse of the Soviet Bloc, there has been a lot criticism of the mainstream communist experience from within the left, mainly from the tenancies of Trotskyism and Left Communism - all the way back to the beginning years of the Bolshevik Revolution. Trotsky criticized the later stages of Bolshevik government and especially Stalin's reign as a "deformed worker's state," where a bureaucratic class had taken power from the organs of worker's power - the Soviets - as well as defeated many of the democratic and progressive reforms that the revolution achieved. Trotsky predicted that eventually this bureaucratic class would "sell out" to a market economy due to pressure and become capitalist oligarchs - as what happened since 1989. Left Communism takes this criticism to a higher extreme - that the communist states of the 20th century were "state capitalist," in which the state and Communist party has simply become the new owning, capitalist class - and the proletariat were in the same fundamental position as workers in the capitalist world. It can be said some of these communist states were resultants of the struggle of the national bourgeois against the imperialism of western capitalism.
No matter what tendency you subscribe to, you still must evaluate the merits of 20th century "Communism" under the light of the historical and material conditions that those states were founded in - backwards, largely agrarian societies that had marginal amounts of industrial capital to begin with. The progress that Marxist-Leninist parties in states like Russia, China, Vietnam are tremendous when you compare to their pre-revolutionary status in terms of healthcare, industry, and living conditions. There were obvious flaws in the history of Soviet central-planning, especially when it came to the information revolution (it is no contest to compare the development of personal computing in the free market compared to the Communist world), but whether that was a matter of historical/material reasons - rather than intrinsic economic flaws - is a matter of debate (would central planning be necessary?) I would suspect that a industrialized, "post-capitalist" socialist society would look radically different from those of past Communist states - especially due to the advent of the information economy, internet, more educated proletariat, and free flow of information.
But, that's really the debate and crisis among the left currently - the crisis of capitalism still exists (more than ever now), and there's plenty of revolutionary and class struggle opportunities abound, however the organized left has collapsed and it currently rebuilding itself - trying to find a new paradigm to fit the 21st century. Some cling on to the old paradigms within Marxism-Leninism, others have discussed radical alternatives to capitalism - and others not so radical. Eventually, I think we're going to find it.
My own opinion, I haven't really formulated one completely yet, and open to new ideas. I think there needs to be a shift from thinking of socialism as monolithic "state socialism" to more of a type of economic democracy of a kind - of course sometimes material and political situations don't allow us to achieve our fullest goals.