It really depends on the circumstances. There are many ways that people in government could handle the collapse of other governments, and military option is far too often put aside in favor of the military option. Still, in the event of an actual genocide occurring, it is our responsibility to help people.
If Government collapses, then it affects more than just the country that has collapsed. It affects surrounding countries and it affects the rest of the world to an extent. With as little aid as we should offer, a path should be set to at least attempt to help these countries from a complete collapse of the Government.
No, I do not believe that we should intervene to prevent the collapse of government in other countries. I think that we should let those other countries handle their own problems. We have too many problems in this country to be wasting money and resources helping countries out that will probably be ungrateful to the help anyway.
Foreign intervention is a waste of time and money - especially at a time in which our national debt is over 16 trillion dollars. (Note that military spending already makes up the majority of our budget.) It's time we started focusing more on domestic issues and less on worrying about what other countries are doing.
When these governments overseas collapse, it is usually because the people in their countries want them to be gone. If you step in and prevent it, you have basically set up a totalitarian regime by default. Their people have spoken and do not consent to be governed by those people anymore. If you step in, then you are acting directly against the will of that country's people.