If you have cedula but you are not naturalized Ecuadorian citizen, you are required now to fill in declaration and have copy of your cedula ready.
If you tourist, make a copy of main page of your passport and be ready to fill in declaracion as well.
here are images of declaracion
Update as of summer 2014: Banco Central del Ecuador has limit exchanging large denominations for smaller ones - foreigners can exchange $200 per month per person. If you have Ecuadorian cedula there is no limit (or so they say)