Do US citizens need a visa for Ecuador and the Galapagos?

No. US citizens can enter Ecuador as tourists without a visa for up to 90 days in total in any 12-month period, and the Galapagos are part of Ecuador, so no separate visa applies.

Your passport must be valid for at least six months beyond your arrival date and have a blank page for the entry stamp. Ecuador can refuse entry and send you back if it does not, and airlines may deny boarding.

The islands add two local requirements on top of national entry: the US$20 Transit Control Card, bought at the Quito or Guayaquil airport, and the park entrance fee, paid on arrival in the Galapagos. You also need a round-trip ticket between the mainland and the islands. Check the US State Department's Ecuador page shortly before you fly, because entry rules change.