A lot of you are partially right.
It all started with this thing called the Cold War and the Cuban Missile Crisis.
The Soviets wanted to place nukes in Cuba. They had some there and JFK knew about it, but wanted to keep it hush-hush from the American people. Russian freighters set sail for Cuba with more nukes, but JFK ordered a naval blockade. He tols Krushchev (the Russian leader) that we'd blow up the ships if they didn't stop. Enter the single most important game of Chicken ever played. Krushchev kept going and going and JFK kept threatening and threatening. If we had attacked them, then Cuba would have launched the missiles they had at us so we would have been forced to fire back and thus, the Nuclear winter would have started and most of us probably wouldn't be around today. Eventually, Krushchev backed off and recalled his ships. Thus, ending the game of Chicken. JFK set up the hot line (a direct line from the white house to Krushchev's office) to start a compromise. Russia had to pull all the Nukes out of Cuba, but we had to pull ours out of Turkey...
By now, we have realized that we needed an ally close to Russia, somebody strong, powerful, and ruthless that would be willing to do what we weren't- somebody to do our dirty work, essentially. Reagan was elected in 1980 and introduced the Reagan Doctrine (an addition to the Monroe Doctrine of yore that basically states the US is the world's police force) that said it wasn't enough to contain the soviets and their silly communistic ways, but we had to confront them with force. So, we headed down to Nicaragua and the Somoza family. They were the ruling family there, a vicious, blood thirsty crime family, yes...but they were anti-communist. In the 1980's the sandinistas overthrew the Somozas, giving Regan ample opportunity to try and arm to the Contras (left over Somozas) to try and get them back in power. Congress shot that down, but Regan found a way around. He sent money to the Contras to buy their own weapons with, and owh, while they were at it, he got us into the Iran-Contra affair. He told them to sell any extra weapons they bought to Iraq and Iran....because they were near Russia. Iraq and Iran have fought for ages, we were hoping one of them would take the other out and become our ally.
But, the Russians invaded Afghanistan! OH NOES! So, we can't stop them ourselves or WWIII starts. So, what do we do? We arm the Muhajadeen (arabic for "The Holy Warriors"...sound familiar?). They beat the Soviets hardcore. But, guess who comes to power through all this? Osama Bin Laden. He was one of the high power members of the Muhajadeen and then formed Al-Queda (the connection)- a network of all his old Muhajadeen buddies.
Then, we had put Saddam Hussein in power because he was ruthless, too and thus, was willing to do anything to the Russians. Oh, and he was anti-communist.
Then, we realized our mistake a few years ago when it started to get out that he was a horrible dictator. We needed an excuse to go in and take him out. "Oh, hey! We're in Afghanistan hunting down one of the guys we put in power in the 1980's....let's take out the other one while we're at it."...."How do you suggest we play that, sir?"...."Oh, let's say he has some WMDs."
And thus, we invaded Iraq.