To recap, if you are coming into Chile by common carrier, you are required to pay a US$100 reciprotict fee (because that is what Chileans are charged for a US entry visa.) The receipt is attached into your passport, and is good for the life of the passport. It is not a visa, nor is it part of your tourist card. If you remove it from your passport, no big whoop, except you will have to pay another $100 next time you visit.

Brazil charges Americans US$100 for a visa - still a reciprocity charge, but for a visa. The only way to get any leverage out of this is to request a "multiple entry visa" when you pay. Mine was good for five years (but had to be activated by my arrival in Brasil within 90 days of having the visa stamped into my passport.)

Every country handles this uniquely - Turkey began charging the $100 reciprocity fee, but is now encouraging tourism by dropping the fee to something more reasonable - it's $20 for a three month tourist visa, as verified to me by Emirhan Yorulmazlar of, I believe, Enformasyon Dairesi Başkanlığı. Good for Turkey! (And Chile does OK too, "for the duration of your passport.")