For 2014, Radicati Group projects 2.5 billion email users worldwide.
How Many Email Accounts?
The mailboxes commanded by these millions of users were estimated to number about 2.9 billion in 2010.
How Many Gmail Users?
In June 2012, Google reported 425 million users worldwide.
How Many Outlook.com Users?
comScore numbers for October 2012 were a bit over 286 million users.
How Many Corporate Users?
The Radicati Group counted 730 million business email inboxes worldwide in 2010, 25% of all email accounts.
Naturally, all numbers are educated guesses. I don't know the exact methods used to arrive at them. Still, they are probably more educated a guess than most of us can make.
How Many Emails?
The millions of email users send hundreds of billions of messages every day.
(Updated June 2013)