1. Communism assumes a degree of altruism which is wholly incompatible with what we know about human nature.
As a result, it is immediately challenged with problems of collective action (the tragedy of the commons, free-riders etc.)
The classical marxist reply to this comes in the form of hand-wave: People are only selfish because they are alienated (Entfremdung). Once the communist utopia has been established, people will cast away their selfish actions and everything would then work. Yet everyone we know about human nature documents that this is an extremely naive view. And such developments have never come to pass in countries that actually try to implement communism.
2. Communism lacks a plausible decision-making mechanism.
Marx popularized the famous claim "From each according to his ability, to each according to his need".
Yet in the absence of markets, the information needed to find out what "ability" and "need" are is almost impossible to come by. The most lethal example of this is the abysmal failure in China of "The Great Leap Forward" which had a death toll due to famine equal to multiple Holocausts (between 23 an 46 million, and probably closer to the latter).
It has actually been established mathematically that highly centralized organizations are incapable of making efficient decisions on complex political issues. This is known as the "Impossibility Theorem", the major reason for awarding Kenneth Arrow the Nobel prize in Economics.
http://en.wikipedia.org/wiki/Arrow%27s_ ... ty_theorem
See also the "Liberal Paradox" by Amartaya Sen (also a Nobel laureate, but for an unrelated work), which is even stricter than the Impossibility Theorem.
http://en.wikipedia.org/wiki/Liberal_paradox
So not only do Communist states lack a way to make efficient decisions, it is impossible to "fix" them and make them efficient.
3. Communism lacks the necessary checks-and-balances to prevent corruption.
Centuries - nay, millenia - of studies on governments have yielded a general view that all political power must not be concentrated in one political office. However, communism introduced a State agency which was basically sovereign: The Politburo. As such, no meaningful division between the legislative, executive and judicial branches of governments was established. This is likely the major reason why people like Stalin, Beria and Mao weren't stopped: Such an organization has no political fail-safe mechanism when a evil person manages to accumulate political power.
4. Communism is a Nirvana Fallacy.
See here:
http://en.wikipedia.org/wiki/Nirvana_fallacy
A lot of people "like" communism because it sounds good. Yet people are evaluating communism on what it says on paper, and not how it will look like if one tries to implement it in the real world. Any real-life political system will look unfavourable compared to "ideal" communism, because "ideal" communism is literally a Utopia of kindness, friendship and love. I think this is why so many teenagers are attracted to communism; they lack the life experience to see that such a political utopia can never be implemented in real life.
Communism: Stick a fork in it. It's done.
EDIT: I actually feel bad for a lot of people who support communism, as they will never ever get what they are hoping for. Currently, the Communist party in Denmark (or the closest equivalent, any way) stands to gain 10 percent of the popular vote at election day. Yet all of these votes will more or less be wasted, because even the party closest to it (The Socialist People's Party) would never lend support to some of the batshit things the Communists have as an official political position. One party official even suggested that they would shut down newspapers that were advocating "pro-business" views if they managed to achieve government office.
... dafuq?