It depends on what the crime is in many cases. The USA would probably extradite to Iran someone accused of murder if the Iranian government could convince a US judge that they actually committed murder. If they accuse them of heresy we won't even if the accused admits it since that isn't a crime here.
Brazil has or had a treaty where it wouldn't extradite for a financial crime if that person had a Brazilian dependent. So commit fraud, make it to Brazil and get married and you were safe.
Some countries won't extradite to the US on a capital case unless we promise to not seek the death penalty.
