Spanish
By far the most widely spoken language in Ecuador is Spanish. Within this, there are three separate, though similar variations depending on your geographical location: Equatorial Pacific Spanish, Andean Spanish, and Amazonian Spanish. Unless you’re a keen linguist, you won’t need to worry about the differences between these as they are relatively unnoticeable to the untrained ear.
Ecuadorian Spanish is spoken slowly and clearly, so it’s one of the best places to learn in the Spanish-speaking world. As in most parts of Latin America, Ecuadorian Spanish utilises the ‘usted’ form as opposed to the more informal ‘tu’ used in Spain.
Kichwa
Kichwa is essentially the northern variety of the Quechua language group which extends from Chile and Argentina in the south up the Colombia in the north. Kichwa has been described as a more simplified version of the the Quechua spoken in Peru and Bolivia - the historical heartland of the language.
Quechua was the pre-Hispanic language of the Inca whose ceremonial capital Cusco, in modern day Peru, acted as a cultural and religious centre for the region. As the empire spread north into Ecuador, they brought the language with them. The version that exists today is less complex than that spoken further south, perhaps due to a ‘creolization’ or intermingling with other pre-Incan local languages. It’s primarily an oral language, which may account for its decline, although these days you’ll sometimes find it written in Latin script.
Chances are you won’t need to learn Kichwa - though if you have an interest in learning it, there are places set up to help you. The fact is that the language is only spoken by around 7% of the population (most of whom are bilingual in Spanish) and its usefulness is very limited, despite it now being taught in some schools.
Other languages
Ethnologue counts 23 separate living languages in Ecuador, though this includes Spanish and as many as 10 sub-varieties of Kichwa. It’s unlikely you’ll come into contact with any of the others on a day-to-day basis, as they’re mostly spoken by small, sometimes disappearing indigenous groups. Many of these groups are from the Amazon region and though fiercely protective of their culture, most of their languages are sadly threatened with extinction.