The trio were suspected leaders of the Spanish operations of Anonymous, a so-called "hacktivist" group that breaks into computers online to pursue an agenda of political activism.
Officers snatched the three suspects in Barcelona, northeastern Spain, Valencia in the east and Almeria in the southeast.
One of the suspects, aged 31, had a server at his home in the northern city of Gijon to run attacks on government, financial and business sites worldwide, police said.
They are accused of hacking the Sony PlayStation online shop, the sites of major banks BBVA and Bankia, Italian power company Enel, and the governments of Egypt, Algeria, Libya, Iran, Chile, Colombia and New Zealand.
A police technological investigation squad analysed more than two million lines recorded on web pages and chats to track down the leadership who took decisions and launched the online hacks, they said.
It is unclear if the suspects are accused of a role in the massive online attacks in April on Sony, which only this month restored PlayStation Network services everywhere except Japan, Hong Kong and South Korea.