Everyone thought that Diablo 3 would be one of the most successful PC games ever, Blizzard confirms this with a report that they sold over 3.5 million copies the first 24 hours after release.
This doesn't include the 1.2 million copies that were handed out to World of Warcraft annual subsribers.
“We’re definitely thrilled that so many people around the world were excited to pick up their copy of Diablo III and jump in the moment it went live,” Mike Morhaime, CEO and cofounder of Blizzard Entertainment
Analyst Arvind Bhatia stated two weeks before the launch that he thought that Blizzard would sell 4 million copies in Diablo 3's lifetime.
After a week there are over 6.3 million people playing Diablo 3.

Source: Gamesindustry
Source: Redorbit