Aside from what SAV mentioned which are a few of the more well known examples of the US propping up someone for their own political/financial interests.
But the thing is that we're already repeating it, we're funding Al Qaeda in Syria for some gain either political or economical. WE're funding the bad guys. The guys who used Sarin gas which is a war crime. By proxy the US is basically committing a War crime.
Everyone claims that Sharia Law is bad and the devil, but the people we're backing in Syria want to implement Sharia Law.
Here's an article to read if you think the US is all sunshine and butterflies
http://www.alternet.org/world/35-countries-where-us-has-supported-fascists-druglords-and-terrorists
Here's the truth you won't admit, War makes the rich richer. So they want a constant war. What better way to do that than constantly overthrow governments by backing extremists, then a few years later after you've made the rounds, oust the ones you put in charge.
That's life. Everyone does that. Every scenario has it's plus and minuses. And America is not fully backing al queda in Syria. There's no american boots on the ground. There's bad guys mixed in with innoncent people with people fighting against Assad. If you give a dollar to a homeless guy on the corner, if he in turn uses that money for drugs are you enabling him to use drugs or do you just do what you think is right and he made a bad choice?
Everybody backs everybody. That's the way the world goes.