May and early June are excellent: the island is green (Corfu is unusually lush for a Greek island, owing to its higher rainfall), the sea is warming up, and the crowds are moderate. Accommodation is readily available and reasonably priced.
July and August are the peak season — large numbers of British charter tourists arrive and the coastal resorts get crowded. Corfu Town itself is less affected than the beach resorts, and the interior (Pantokrator, Old Perithia) is largely tourist-free even in August.
September and October are particularly good. The summer crowds have thinned, the sea is warm (its peak temperature comes in September), and the light is excellent. Many Corfiot families take their holidays in September.
November through April is the wet season. Corfu receives significantly more rainfall than the eastern Aegean islands — the olive trees and cypress forests depend on it. Some beaches close and ferry services thin out, but the town has year-round life and accommodation is cheap. The island is genuinely green in spring, which can feel startling after winter in northern Europe.
The Corfu International Film Festival runs in October; the Corfu Beer Festival in July is a notable if peculiar event. Orthodox Easter (variable date) is celebrated with particular intensity on the island, including the famous pot-smashing ceremony.