Ecuador is divided into three distinctive climatic zones (four, if you count the coast and Galápagos as separate).
Quito & Highlands: Quito is broadly representative of the climate in the Highlands region and it is still the height of rainy season here. In fact, overall March is the second-wettest month in this region. In Quito, March has the lowest temperature variation of any month with the highest average lows. But the rain is heavy: 6.4 inches (163mm) is a monthly average.
Oriente/Amazon: Ecuador's Amazon climate varies because this is a vast region. In Parque Nacional Yasuni, the most popular destination for travelers, rainfall increases dramatically in March to in excess of 8.46 inches/ 215mm, although the weather will not get warmer than it is now until November.
Desert Coastal Strip & Galapagos: On the coast, it is sunny and warm, despite this being wet season: rain usually comes in the afternoon for short periods, but mornings are usually bright and with brilliant sunshine. March is sunny and wet in the Galapagos Islands, although signs of the impending dry season are already evident, especially in the behavior of the wildlife.
Crowds & Costs
Easter, and the Semana Santa (Holy Week) that precedes it pull in the crowds for part of the month, should Holy Week fall in March. And the main coastal destinations remain busy as high season continues. However, elsewhere, volumes of travelers are far below the North American/European summer holiday season highs, which can make for more peaceful exploration (and cheaper rates) in the Highlands, Galapagos, and Oriente.
Where to Go
Quito & Highlands: Cool, wet weather persists through March. However, this does not matter so much if you are exploring Ecuador's superb cultural heritage, and the fabulous colonial churches and museums of Quito or Cuenca are great for exploring at this time. Quito has one of the best Semana Santa celebrations, should Semana Santa fall this month. Or head to the cloud forests around Mindo, where some of the year's best birdlife is on display.
Oriente/Amazon: This is a good month for exploring Parque Nacional Yasuni. An increasingly wet month like March means much wildlife evades the water levels and takes to the trees, so it is easier to see. The towns of Tena of Baeza, with great white-water rafting, are good to visit now.
Desert Coastal Strip & Galapagos: March is the last truly great surfing month in Ecuador, so head to the likes of Mompiche or Montañita for the big breaks. Or on the Galapagos, head to Isla Isabela/Isla Fernandina respectively to see the land/marine iguanas nesting.
What to Do
Quito & Highlands: It is a good month for indoors sightseeing in the highlands: checking out one of Quito or Cuenca's superb museums or churches, for example. Or catch one of the many festivities starting to happen across the Andean zone this month, as Semana Santa festivities get going.
Oriente/Amazon: This is a great time to go white-water rafting in Tena, or perhaps Baeza. March starts to be a good time to visit Cuyabeno Wildlife Reserve, in the Northern jungle. Paddling by canoe, one of the special highlights of this trip, becomes possible again as Cuyabeno's wetter season weather fills up tributaries.
Desert Coastal Strip & Galapagos: Try surfing whilst the season is still perfect for it at a coast town like Mompiche, or sun-bathing anywhere along the Ecuador coast's sandy beaches. Wildlife watching in the Galapagos is always fascinating: in March, watching turtles and iguanas nesting is especially memorable. Calmer waters also make for good snorkeling on the islands.
Semana Santa (Holy Week): Religious processions fill the streets of main towns and cities with a beautiful solemnity in this week leading up to Easter in March, should Easter fall in March.
Mushuk Nina: March 21. This is Andean New Year, celebrated only in a few places with strong Andean roots, such as the archaeological site of Ingapirca near Cuenca. Held to celebrate the spring equinox, it involves rituals including smoke-cleansing, performed by shamans, and lots of traditional music-playing. It's a great festival for experiencing local mountain culture with few other foreign travelers around.