Your average game development studio would have a heart-attack if they found out they sold one-million copies within a year, but Blizzard Entertainment isn't your average studio. Five-million units sounds about right.
Doug Creutz of Cowen & Company estimates that Diablo III will manage to sell five million units within its first 12 months. A fifth of those sales will come from World of Warcraft's 'annual pass' system which offers Diablo III at no extra charge.
For comparison's sake, StarCraft II sold around 4 million after its first year, while World of Warcraft didn't have four-million total subscribers-to-date until nine months after launch. Better yet, Diablo II: Lord of Destruction still hasn't sold five-million copies in its lifetime. Needless to say, this estimate is extremely high, but if any any game of 2012 is going to do it (excluding Call of Duty), Diablo III is it if hype is any direct indication.
The addition of console versions should boost the numbers tremendously, but no release date for platforms outside of PC has been revealed, so this prediction is aimed directly at the PC version which will debut on May 15th.