Diablo III has been selling incredibly well. Sales numbers for the first week, let alone the first day, have been absolutely unbelievable. I'm sure part of that is due to the fact it has taken Blizzard so long to release this sequel. The other contributing factor would be the absolute quality of the game as seen in the demo.
Sales on the first day totaled 3.5 million copies. That yields about $210 million in revenue. That number doesn't include the 1.2 million players who received Diablo III as part of signing up for World of Warcraft for a year. In total, an incredible 4.7 million users purchased the game within the first 24 hours it was available.
By the end of the first week, Diablo III had sold 6.3 million copies yielding a rough revenue of $378 million. Wow. With incredible uptake numbers such as those, its clear why Blizzard's servers have been getting hammered and giving players trouble logging in.