Given the frequency with which this word is bandied about nowadays, it's amazing just how little agreement there is on exactly what constitutes unilateralism. In the popular press, the word could mean either "doing what needs to be done, even if we must stand alone", "protecting our interests", "acting selfishly", or "acting in a manner which is likely to destroy civil society", depending on the point of view of the author. In the mouth of politicians, the word usually seems to mean "acting in a way I don't like".
From a non-ideological and theoretical perspective, unilateralism is a lot easier to define. There are two ways in which the relations between countries can be governed. First, you can have a transnational rule of law, setting out the principles according to which countries are supposed to conduct themselves, and the rules according to which any conflicts will be settled. Second, you could have a situation in which each country decides how it wants to act, and the rules by which it will play. The first situation is what is normally called "multilateralism" or "internationalism". The second is what is called "unilateralism".
Ye Olde Unilateralism
Clearly, no civilised society would let its citizens behave unilaterally and get away with it. Why then is unilateralism tolerated, and even vociferously advocated, at the international level? The answer is that our inherited tradition of pragmaticism holds that it is unrealistic and unreasonable to expect countries to behave altruistically. Governments exist only to serve their citizens' interests, and it is not their business to watch out for the citizens of other countries just because their own governments aren't able to.
As any schoolteacher will tell you, if you allowed the same thing to happen in a schoolyard, it'd quickly be taken over by the biggest, strongest, and nastiest lads in the lot, who would then spend the rest of their lives merrily oppressing the weaklings. For generations, pragmatists argued that this would not happen in the international realm. They said that countries could take comfort from two things. Firstly, there were some basic rules, which countries had to stick to. These were things like the Geneva Conventions, the respect for neutrality and so on, which protected weaker countries against the worst abuses. Secondly, because there were a number of Great Powers, none of them would be allowed to get more powerful than the others. This meant that the world had a Balance of Power, which maintained itself. Ergo, weaker countries could protect themselves against predators by allying with one or the other Great Powers.
Unfortunately, this comfort proved to be illusory. The much-touted basic rules covered only a few, select points which the Great Powers felt did not adversely affect their long-term interest. Countries proved quite good at ignoring the spirit of the laws and adopting readings that served their interests. The rules, for instance, didn't protect the countries of the South and the East from the horrors of colonialism, or, in more modern times, from being turned into pawns in the games of the superpowers.
The balance didn't work either. There seems to have been some existing or wannabe Great Power at any time that was unhappy with its position in the world, or that thought it could suddenly improve its position in the world (see the Napoleonic Wars and the Crimean War for a time when all the Great Powers got into the game). Newly unified countries like Italy and Germany under their youthful emperor and kaiser were particularly good at trying to leapfrog their way up. The best way to do this was by winning a war. The result: between the battle of Waterloo and World War II, when a balance supposedly existed in some form or the other, we had about 325 wars with almost 30,000,000 direct battle-related deaths, and a horrendous amount of civilian suffering.
A more "altruistic" unilateralism
When the struggles between the powers produced World War I, it ought to have brought home the failure of unilateralism to produce a peaceful, stable polity. Amazingly, it didn't. The Treaty of Versailles and the League of Nations aimed only to shore up the powers of the victorious states and punish the defeated - a classic balance of powers outcome. Predictably, twenty years later, there was another, much bloodier, conflict. At least now, they'd learnt their lesson, hadn't they? By creating the United Nations, an attempt was made for the first time to put in place and uphold a system based on rule of law and on rules of conduct agreed to by all which would, eventually, produce a more stable, predictable, and prosperous world; one which would be a viable and effective alternative to the chaos produced by a cacaphony of foreign policies based on unilateralism. Right?
Unfortunately, not quite. The name "United Nations" was first used in 1942 in a declaration of 22 nations fighting Hitler. It was substituted the original proposal of "Associated Powers" because it sounded better, and it was nicely remniscent of certain lovely lines from Byron's Childe Harold (check Canto III, verse XXXV). However, the attitudes that lay beneath the original proposal didn't change, as we can clearly see from the behaviour of its members during and after the Cold War. Effect: voting in the UN itself was based on interests and alliances; UN decisions reflected acceptable compromises rather than principled applications of a rule of law; and... (surprise!) unilateralism received a new fillip. Because the UN was not effective enough, the new unilateralists argued, to be able to create a new international order, it was the countries with power which would have to do this. If they had to step outside the framework of international law (such as it is), morality, and the UN to achieve the greater common good, then so be it.
The effect of this doctrine was - over time - to erode the stature of the UN. Consequently, when the Cold War finally ended, unilateralism did not vanish. Instead, people such as Senator Jesse Helms argued that the US as the only remaining superpower need not bother with international law. The US' freedom to act should not be circumscribed by anything other than its Constitution. Letting the UN, WTO, or any other international organisation dictate terms to the US was insulting, and an infringement of its sovereignty. This radical attempt to return to old-style unilateralism has had a noticeable effect on Congress in both the Bush and Clinton administrations. The refusal to engage globally on climate change and the Helms-Burton Act are two examples.
Other countries have followed quite happily in the US' footsteps, notably in the third world, where a revival of anti-European post-colonial political rhetoric is already increasing popular sentiment against the west. As if that weren't enough, a significant section of Europe quite quickly positioned itself in opposition to the US. Result: a fresh polarisation in the UN, and once again, voting and decisions reflect compromises and narrow national goals rather than a genuine desire to build a sustainable system based on the rule of law. Witness the UN proceedings during the Kosovo crisis (which ended in NATO intervention without direct UN authorisation) and the Iraq War (which ended in Anglo-American intervention without express UN authorisation). Incidents like these have strengthened the arguments for unilateralism, even sparking a revival of the suggestion that the US must act unilaterally for the greater global good.
The dangers of unilateralism
The problem with the revival and growth of unilateralism is that it is counter-productive, if our aim is to solve the problems the world is facing today. The environment is fragile, and deteriorating. Weapons of mass destruction have spread alarmingly, so that private individuals now pose as much of a threat to security as national armies. Poverty, hunger, and disease blight the lives of a good section of the world. The "scourge of war" which the UN charter sought to banish forever continues to haunt the world and destroy the lives of people. These problems aren't going to be solved without international collaboration. Instead, the EU, the US, and the third world are more divided today on most key issues than they were during the cold war, with allegations of 'bias' and 'hidden agendas of self-interest' flying back and forth quite regularly. Anything short of an international rule of law is only going to give more grounds for this.
Even terrorism is not going to be solved by one country acting alone. The military might of one bloc of countries cannot by itself cope with networks of individuals who're not connected with any state - a government can be bombed into submission, but a sufficiently diffuse network can't. Nor can traditional state-to-state diplomacy help, because the antagonists here aren't states. A framework of institutionalised international collaboration which draws all countries into networks of cooperation and consultation is the only realistic way to effectively tackle this problem. Furthermore, a grievance of many terrorists - certainly of a good section of the Islamic ones - is that the powerful countries are exercising hegemony on the rest of the world. Acting unilaterally only reinforces that, and helps them win more recruits.
Finally, even on a narrow view of self-interest, unilateralism is a bad idea in the long-run. Historically, no country's power has lasted forever. Sooner or later, the balance is going to tilt against the dominant powers. Unilateralism doesn't protect against this. On the contrary, it actually removes the safeguards that an international rule of law would have provided.
In the early days of the UN, actual progress was made towards creating the sort of international system that could actually address these issues. Moving towards it and away from unilateralism again is really just a matter of taking up where we had left off when interrupted by the Cold War. It's not like the world has very much of a choice, if we want to do more than pay lip service to the ideals of security, prosperity and justice for all.
This material for this writeup comes from a tiny section of a lecture I gave some months ago about the Arthashastra's take on contemporary problems in international law. The writeup itself is not based on the lecture - it's been written from scratch in deliberately non-academic language for a non-specialist audience. I'm quite prepared to answer criticism and differences of opinion, so feel free to respond.