Most nationalities, including citizens from the EU, US, Canada, Great Britain and Australia don’t need a visa but only a passport valid for more than 6 months. Most airlines will also ask you for a return ticket at check-in to your flight to Ecuador.
The tourist visa you get upon entry is valid for 90 days per year. Multiple entries are possible. It can be extended to a 180 days for a fee (132$ at the moment). For example at the migration office in Quito (Av. de la Republica y Av. Amazonas)
But, be careful! If you overstay you might be fined and/or banned from re-entering Ecuador in the near future.
Citizens from countries that need a visa issued beforehand are:
Afghanistan, Angola, Bangladesh, Cameroon, Congo, Cuba, Egypt, Eritrea. Ethiopia, Gambia, Ghana, Guinea, Haiti, India, Iran, Iraq, Kenya, Libya, Nepal, Nigeria, North Korea, Pakistan, Philippines, Senegal. Somalia, Sri Lanka, Syria, Venezuela, Yemen, Vietnam.
Most nationalities are able to enter the country with a 90 day tourist visa.
You can find here updated information about Colombia’s visa policies.
From around 100 countries the citizens may stay up to 90 days within 180 days.
For other nationalities check this link.