Hitchhiking in Ecuador
It sounds like a great idea, unfortunately it is hardly ever a great success in Ecuador. Ecuadoreans don't hitchhike and it would be considered strange if you did.
Besides being strange, it can be dangerous too. The roads of Ecuador are not always the safest place to hang out, and not all Ecuadoreans can be trusted around your western riches. Female travellers should certainly think twice before starting their hitchhiking adventure.
The only place to hitchhike is in the countryside where there are no other ways of transportation available. Getting on the back of a jeep is generally accepted in those areas. If you get a ride, it may not be free. So ask the driver after he dropped you off if he wants something in return (quanto lo debo?).