Pretending to do stuff and be important since 1945.
The League of Nations
World War One started because Gavrilo Princep wanted a sandwich. Because everyone in Europe had different alliances and treaties, the more powerful countries were forced to enter the war because the treaties were more or less binding. So what could have been simply a small regional conflict erupted into the biggest war the world had ever known. As with most major wars, many new kinds of weapons were introduced, including the first chemical and biological weapons used in large scale combat.
Your face... after mustard gas.
Sooner or later, the United States got involved and thousands of fresh troops beat back the Central Powers, led by Germany. The whole world sat together and agreed that the war was all Germany's fault and that they should pay for all of the damages the war caused. The many nations of the world liked this idea and decided to sit down and blame stuff on other people more often. Thus the League of Nations was formed.
There were several main problems with the League of Nations. America refused to join because Woodrow Wilson was pissed at everyone when they refused his Fourteen Points of Peace and just decided to blame Germany. Germany wasn't allowed to join because the Great War was all their fault (They were allowed to join a few years later after a lot of ass-kissing). So, two major nations were not a part of the league. They tried to make everyone learn Esparanto. The biggest problem, though, was that, for any decision to be made, there had to be a unanimous vote in favor.
That's right, any small island in the middle of the pacific could go to the League of Nations and vote down a measure and screw it up for everyone else. Also, if your country attacked any other country, you were kicked out. By 1935, the only countries that mattered that were still members were France and Great Britain. Then Germany invaded Poland and the League fell apart.
WWII and the Birth of the United Nations
The Second World War was entirely the fault of the League of Nations wanting to blame everything on Germany and believing that there would never again be wars. We all know how that worked out.
Pictured here: "Peace in our time"
So, after the war was over, everybody sat down in a group and talked about their feelings. They decided that they needed to prevent things like the Holocaust and Nuclear Warfare from ever happening again, So they formed the United Nations, where all the countries of the world could sit down and talk about their feelings. They fixed a lot of the problems inherent in the League of Nations. Only the important countries (UN Security council) could vote on issues. Every country that mattered and almost every country that didn't joined the UN.
Therein lies the major problem. Since the world was divided between the communist countries and the capitalist countries, both sides having nukes, the UN couldn't ever rule in favor of one particular group without causing nuclear war. So, all UN measures and resolutions are designed to try to avoid problems, rather than solve them.
The Creation of the Nation of Israel
Undoubtably the biggest failure in peacekeeping of the UN. The UN gave the Zionist Jews a hunk of land after the Holocaust. This hunk of land included Jerusalem, one of the holiest cities to three major world religions (Judaism, Christianity, and Islam). The biggest problem of this was that Israel did not have contiguous borders, meaning you had to cross through the nation of Palestine to get to the other parts of Israel. The UN did this because they wanted to separate the Jews and Arabs, but didn't want them to incovenience them by making them move far. The Jews weren't too happy about this and decided to just take over all of the country. This, in turn, pissed off the Arabs. Every country around Israel invaded them at once, then Israel beat off all of them. The Arabs continued terrorist attacks against Israel until the '70s. The Yom Kippur War had almost every islamic country fighting against Israel. Israel then hulked out and expanded their borders by over 200%, capturing the Sinai Penninsula and Golan Heights.
They later gave Sinai back to Egypt in exchange for a binding peace treaty. Needless to say, there is still violence every day in Israel. All because of the UN.
During WWII, while the United States attacked Japan from the Pacific, the Soviet Union worked to clear the Asian mainland from Japanese influence. They got halfway throught Korea when the war ended. The North half of Korea became a communist dependent state of the Soviet Union, while The United States took care of rebuilding the southern half. Both sides of Korea wanted the whole penninsula under one government, so they could see their families more easily. The problem was, those in the North like Communism, while those in the south like Democracy. So, they started to fight eachother to reunify Korea under one government.
Then the United States and Soviet Union got involved, each supporting their respective sides. The US and South Korea nearly succeeded in reunifying the continent, then China got pissed because all of the Koreans were flooding into their country and they didn't like that. So China got involved and pushed South Korea back to the 38th parallel. Then the UN got involved and drew a line there, telling both sides not to cross that line. Both sides did anyway and continued fighting, but neither side was getting anywhere so they signed an armistice, not a peace treaty, an armistice. Which means that we are still technically in an active war with North Korea, we just aren't shooting at eachother. Both sides still hate eachother and are trying to plot to destroy eachother.
When Rwanda gained its independece from Belgium, there were two major tribes; the Hutus and the Tutsis. This is all Belgiums fault because in the 1800s, they separated the population by deciding which black people looked the whitest (Tutsis) and put them in political positions because they wanted to be progressive, but were still just as racist bastards as the rest of Europe at the time and didn't want any "dumb Africans" (Hutus) running the government. So the two tribes were formed and for a long enough time, they just didn't like eachother. After Rwanda gained its independence, the two tribes started fighting. The UN sent a peacekeeping force to Rwanda to calm the violence, except the UN soldiers were not allowed to shoot anybody, no matter what. So essentially the UN peacekeepers were there to make sure that the UN peacekeepers didn't get shot. Then the infamous Rwandan Genocide broke out and the UN troops retreated, so they wouldn't get shot. It was all up to Don Cheadle to hole up in a fancy hotel and try to save as many Tutsis as possible.
Yet again, the UN was proven useless in a national crisis.
Separating the Hindus and Muslims
After India won its independence, it was a land split between the native Hindu population and the emerging Islamic movement. They didn't like eachother. The Muslims hated the Hindus because they worshipped many different gods and none of them were their god. The Hindus hated the Muslims because they told them their religion was wrong and heathenous. They started fighting eachother and the UN stepped in. They drew lines and separated the two religions. The Muslims were forced to move out and go to either East Pakistan (now Pakistan), or West Pakistan (now Bangladesh). All of the Hindu living in East or West Pakistan had to move to India. This was one of the biggest migrations of people in modern times, millions of people packed up and moved to the land desgnated for them by the UN. Neither side liked the borders the UN gave them, so they started fighting again. India reclaimed West Pakistan and they are still fighting over Kashmir. Now both sides have Nuclear Weapons and are essentially in the middle of their own Cold War.
Iraq weapons inspectors
Ever since the First Gulf War, The UN had been telling Iraq to disarm their WMDs that they had tried to use on Kuwait and Iran. Most of these were chemical and biological weapons left over from the genocide of the Kurds. Sadaam Hussein just simply said no. He continued building weapons at least through 1997. After 9/11 the US was very paranoid about Arab nations having weapons of mass destruction. President Bush called for UN weapons inspectors to make sure that Sadaam Hussein had disarmed the weapons that the UN had been telling him to disarm for ten years. The problem was, the UN only gave the inspectors the authority to check where Iraq said it was OK and they had to give a few weeks notice. Due to this, the only conclusive evidence of Iraq's WMDs was found years later by US Soldiers. Because of the UN's inablity to properly search for WMDs (and because of a intel leak that turned out to be false), The United States invaded Iraq, killed Sadaam, and is still there rebuilding. After the violence had calmed enough, US soldiers went looking for the WMDs and found shipping manifests that said they had shipped across the border to Syria while the UN weapons inspectors were inspecting.