Well... basically everything. And nothing. It depends on the government implementing it. Russia was "communist" and failed - because it wasn't really communist. China is pretty damn successful (they're exporting like crazy) because they're implementing it in a lax way. But they're not really "communist" either.
If with "communist", you mean the government described by the original Marx and Engel, forget it: It's not going to happen. It's outdated. We live in a post-industrial society. Information is more important than goods by now. We have machines for that. Marx was hoping for the worker's revolution - the time is WAY
past. 1846 AFAIK was the date that he thought it was going to take place. It's been more than 150 years, and still no "communist revolution" has happened. And the era of industrial communism is virtually over. China maybe, but even they are developing into a more information and services based economy.
If with "communist" you mean an economic system based on the distribution of services and goods to everyone equally, it's not going to work out either. The system is based on trust - trust on the government to implement a policy that will not put their ego in front of the people. So far, I haven't heard of a single government actually implementing this. So really - there's never been a country that has been, economically at least, communist.
Another problem with economic communism is, that you need people to work. No matter what. Be it for information based servives, for industrial labor, for the public sector, whatever. Even in the unlikely case that somehow everyone gets equal pay and equal benefits from the government, it is BOUND to fail - there would be no motivation to work, the economy would slow down to a halt. Also, there's no incentive for investing into new stuff, no incentive for start-ups, no incentive for export.
A compromise between communism and capitalism would be socialism. Socialism, however, HAS failed. History shows that socialistic states (USSR and it's satellite states) do fail. Socialists assume that everyone starts out equally and then does the best from there onwards (i.e. minimum wage, even for people not working). However, it requires constant export and a good balance of trade, or the economy will impoverish itself. Unlike in capitalism, the economy cannot be fully integrated into international markets, because the state controls most of what goes on in the economy, at least on an internal level.
Here's a diagram of my "compromise". It has several flaws though, which I'll get into later.
The f(x) thing is basically a function that takes into account the current internal economic situation, the actual work the consumer has done, and the money available to the government. It will not reach 0, there is a minimum which is paid even IF there is no work done (just enough to keep you off the streets, but little enough to give you motivation to find a job). It also "removes" taxes and the dreadful deadline to fill out your forms, with the government ensuring that there is as little taxation as possible. It's in it's best interest, if not the economy will go sour, people will stop working (no money? HEY... I'm NOT working for nuttin'), there will be no more returns from the companies set up, basically the gov. will be stuck with ~ 1/3 the money in the system, the rest being in the companies and with consumers.
- Consumers MUST consume. If they don't... Investment money is lost, or the money stays with the consumer and rots away in a bank vault. Of course, he could also invest into a private firm.
- Here we get the problem of PRIVATE firms which are a major source of cash leakage out of the system. Repossessing them seems a bit harsh, so how about heavier taxes once they reach a certain size?
- There MUST be a good labor market. Employ too little people, and the system crashes, with the government owning all the money. Again, the government creates jobs by investing into start-ups, which brings me to the next point:
- There MUST be a benevolent government. That's the key. If the government goes all egomanic, there's a good chance there will be no more investment, the function is abused (essentially slave labor), deficit.
- The nations must be able to support itself and keep the money in the state. Or, alternatively, a good balance of trade must be present. Otherwise it's the same money cycling all over, with no net growth.
Capitalism is just as bad. If people manage it too much, constrain the banks, make bad choices, keep money out of the cash flow, it's just like the "government" in communism keeping the good stuff to itself. Money has to be kept in flow. Communism kept it behind an iron curtain. Socialism tries to accommodate, but ultimately, it's a cheap compromise relying on the hope that the system won't crash and that there will be export.