Ecuador sits on the Equator and as such she has similar weather all year round. As the country incorporates the Galapagos Islands, you will find small seasonal differences.
The small rainy season runs from January to March, especially in the Galapagos Islands, though this can be a time when a barren volcanic land springs into life. On the mainland expect year round good weather with the occasional shower. Specific drier months are June to September.