Many people have a blind faith in pure capitalism and an irrational fear of socialism. Pure socialism doesn't work, we've seen the system prosper and then collapse completely within 50 years during the cold war.
However capitalism by itself also fails, it just takes longer. Many countries throughout history have had capitalist systems, and all many have fallen apart.
In order for a system to work it needs a bit of both. In United States is one extreme where the system is nearly entirely capitalist with very little control of business by the government, China is the other extreme by which it is nearly totally communist, but has rudimentary free markets.
Both are working (The US is doing better than China, but China's system doesn't look like it will collapse any time soon.)
Capitalism means that the free market decides everything. A pure capitalist system doesn't exist as far as I know. It assumes that companies that produce the best products will grow and companies that produce poor products will fail.
The US balances a free market with some socialized systems. Schooling is free, fire and police is free, however there are also private alternatives. England, Canada, Russia, France... provides health care for free and France provides nanny services for free.
The problem with pure capitalism is that it assumes the best in the CEOs. The problem is that greed takes over. The best example that I can think of is Microsoft. During the 1990s Microsoft came out as the dominate software developer, because (at the time), they were the best.
Other companies with better products started cropping up. The free market should have boosted these companies, however Microsoft bought them out before they could get big and the superior technology was never seen again.
Pure capitalism + greedy executives results in monopolies, which is the fundamental opposite of capitalism. The book 1984 shows what could happen if an individual company was allowed to grow without interference by the government.
Greed also can make companies exploit people's needs. Supply in demand is the basis for capitalism and will work within reason, but if demand skyrockets, companies start to exploit people.
The Pharmaceutical companies are the worst case of this. Pills that cost cents to make end up costing dollars in the american market. The same drugs are 50 times cheaper in Cuba than the United States because the market there is controlled by the government as it is in most of the developed world.
I mentioned in another post the gas companies, they do the same thing. People need gas to get around, so prices are hiked up beyond reason. The price of oil has been going up for other reasons, however the price of gas is going up faster than the raw oil prices because of the fact that it is running without check.
When companies get rich through capitalism, some try and shut it down. The oil companies and the pharmaceutical companies pour massive amounts of money into Washington to keep the free market from bringing them down. The more powerful a company gets, the better it can do this.
Pills are the best example of this. Many americans used to buy their prescriptions from Canada because they were far cheaper. The free markets says that they should be able to do that, however the powerful drug companies lobbied Washington and made it illegal to get cheap drugs from Canada.
I hope this was informative. I wrote it fast, so if you see any mistakes let me know and I'll fix them :)