is the proposition that a society should be run in such a way as to share the benefits fairly among all its members. Obviously the interpretation of what is fair is at the root of the questions to be asked.

These are only a few of the questions to be answered.

Yes, I am a socialist. No, Hitler, Stalin, and Lenin were not socialists.

The issue of how to increase the benefits of society is not strictly implied by socialism, and indeed the question of whether industrial progress causes net benefits is disputed in some places, but most proponents of socialism maintain that it does increase the quantity of benefits to go round.
Three issues are topical today in the year 2009 CE, in the USA:

Solutions are being proposed, and shot down in the "debate", by the "spectre" of Socialism.

I do not know how many people have noticed, but the mess in all three of these issues has been noticeably coincident with a great increase in the relative power of very large corporations, and their failure to do a good job. In fact they failed to prevent exactly the bureacratic incompetence, and the managerial arrogance and corruption alleged to be endemic to entrenched Government Departments.
But there is considerable evidence that FDR rescued the USA from the Depression by following remedies that are suggested by the work of the economist John Maynard Keynes. They were regarded, correctly IMHO, as essentially socialist. Keynes pointed out that paying people for merely digging holes in the ground can improve prosperity. It doesn't really have much to do with the trifling intrinsic usefulness of the gold or diamonds dug up.

The Free Market

There is still a belief that unregulated private enterprise is bound to do a better job than "Government".
It is based, perhaps, upon Adam Smith's conclusion that a free market would serve all parties best and most fairly. But the private sector today does not meet Adam Smith's criteria of a free market. It is dominated by corporate enterprise which is highly oligopolistic even to the point of monopoly and monopsony. monopsony is the condition where there are many vendors, but only one buyer.

One instance of the flaw in the belief is that whereas the US Department of Justice proved in court that Microsoft had monopoly powers, and could not be trusted, the electronic data processing policy of the US Department of Justice, and of a great many others, is itself governed essentially by what Microsoft Corporation decrees. This shows the hold that Microsoft has upon the data processing apparatchiks of the DoJ. Microsoft governs the federal Government and many huge corporations in this respect, so reducing the power that the Federal and State governments have will not improve our liberties at all— especially if the power that we cut is our government's power to curb behemoth corporations.

Things that private industry cannot do efficiently:

Scientific Research

Alan Greenspan has admitted that his philosophy of total trust in an unregulated market, governed by agreements undisclosed to outside parties, is false.
It follows that the presumption that private enterprise can always be more effective than public enterprise is wide open to question.

Now we know that in scientific research, private secrecy is a hindrance.

The great search of the alchemists for a way to turn lead into gold was an utter failure, not just because it's impossible by the means they were using, but because you cannot make money from being one of the world-ful of people who can turn cheap lead into precious gold. If it's easy, and widely known, it's no longer profitable.

In Napoleon's time, aluminum was more precious than gold. Now that we can make it (fairly) cheaply by electrolysis, it's cheaper than tin.

For the purpose of building a gravitational wave observatory, Kip Thorne of Cal Tech wants two perfect cylinders, a kilogram each, of synthetic sapphire or ruby.
We can probably synthesize diamonds better and cheaper than the natural ones. Companies like de Beers are desperate to find ways to identify the difference.

Thus the motive of private proprietary profit obstructs the flow of information that a healthy world science needs to thrive.

Nuclear power

comes from fissile nuclides, of natural uranium, and synthesized plutonium. The commonest fissile isotope of uranium that occurs in nature is isotope 235, which is only 0.7% of uranium. It is chemically identical to the common isotope 238, but for reactor use it needs to be concentrated to about 5%, by a process called "enrichment". It is a physical process, like making brandy from wine by distillation, if the boiling point of alcohol were about two degrees Fahrenheit lower than that of water.

To explore the various plausible ways of enriching the proportion of this isotope is very expensive, and must necessarily cost society at least five times as much, if five commercial organizations with patents and trade secrets all do it in competition. Fortunately for the world, it was too difficult for Hitler's Germany before 1945, in spite of the fact that two or three of the world's most brilliant atomic scientists were still in Germany. But once the Bomb proved it possible, the Soviet Union was able to discover a way.

Britain even got itself an 'Independent Deterrent', just in case the USA might think Britain too insignificant for the thought of starting the Third World War against the Soviets. So did France.

In the absence of an international government sufficient to punish nuclear-minded evildoers, the Nuclear Deterrent now works for Iran and North Korea, and we can deduce that Iraq was known not to possess it.

Scientific Research

In general, scientific research at a deep level is hampered by the necessities of proprietary profit. But public, published science is of immense value to society.
The causes of malaria and yellow fever were discovered by the British and the American governments respectively, in each case by medical doctors in the armed forces.

I am using the most powerful computer complex in the world, as are you, the reader.
It is an abstraction called the World Wide Web, and was initially devised as a way to exchange scientific information using the machinery of the Internet.
It was publicly invented, by nuclear physicists, at the European Center for Nuclear Research.

One of the things that can actually be done with it, and is being done, is to allow people to volunteer unused processor time on their own computers, to be used as part of some chosen computationally-intensive project. This makes a virtual supercomputer available to the project, at near-zero cost!