This can depend on where you are going. In most of the country, the main rainy season runs from June to the end of September, with short rains in March. In the Omo and Mago parks however, in Southern Ethiopia, the seasons are different with the main rains from March to June, and shorter rains in November.
With the upgrading of the airports along the historic route (Axum, Lalibela, Gondar and Bahir Dar), it is now possible to visit the north even in the rainy Sean. For travelers who do not mind waiting out a downpour (usually followed by brilliant sunshine) there are certain rewards-a green countryside full of crops and flowers and the sites largely to your selves.