Step 1: Recall what OPEC is.
OPEC, the Organization of the Petroleum Exporting Countries, is a group of oil producing nations that work together on output and pricing policy.
Step 2: Check each country against the OPEC member list.
Algeria joined OPEC in 1969 and is a long standing member. Ecuador joined in 1973, left in 1992, then rejoined in 2007, so it counts as a member country. Nigeria joined OPEC in 1971 and remains an active member and major oil exporter.
Step 3: Look at Brazil.
Brazil is a large oil producer through Petrobras, but it has never joined OPEC. It has stayed outside the group so it can set its own production and pricing policy.
Final Answer:
Brazil is the country that is not a member of OPEC. \[ \boxed{\text{Brazil}} \]