Argentina: You may visit Argentina for up to 90 days on a tourist visa by just showing a valid U.S. passport when you arrive. For a residence visa you must have a passport valid for at least six months longer than your arrival date. You may need a physician's report to ensure you are in good health. You may also need a criminal background check, depending on the consulate where you apply. These documents must be translated into Spanish and notarized. Check with the Argentine consulate where you make your visa application for acceptable translators and notaries.
Brazil:
any foreigner looking to work in Brazil must have a work visa or Brazilian residency. In most cases, you should have a job secured before planning to move. The employing company must submit a work permit application to its local Ministry of Labor & Employment – this is the first step to meet the requirements in the work visa application process. After the application is approved, the approval is published in one of the local legal newspapers and sent to the Ministry of Foreign Affairs. After this, the Ministry will contact the Consulate or Embassy, which will then start the visa process.
No. Even South American countries don't have any open-door policies.
Argentina's process sounds easy enough to me, and similar to Uruguay's, which is where I'm from. Of all things you have to do to move to a whole 'nother country, a fair dose of paperwork should be fairly low on your list of worries.
You will do about as much if not more paperwork when trying to rent a place, sign-up for electricity, Internet connection, a smartphone contract, and so on.
So it does seem to me that TurkishPoptart is fairly free to leave if his/her worry is just complying with the law as mentioned in the posted comment.
EDIT: Guess you guys didn't want to move after all. We'll still welcome you if you change your mind.