Last week, Paul Allen (founder of Ancestry.com) put together some estimates claiming that Google+ was getting ready to pass 10 million users, and on pace to soon hit 20 million. Shortly thereafter, Google CEO Larry Page announced officially that the service did indeed pass 10 million.
So, Allen seems to have a fairly decent methodology.
"Last week we saw two days where more than 2 million signed up in a single day," wrote Allen. "If that rate had continued, Google+ would have reached 20 million users by last Sunday night. But the last four days have averaged only 948,000 new users and yesterday the site added only 763,000. Yesterday's growth of 4.47% was the slowest viral growth since Google opened up invites back on July 6th."
He also included the following graph:
Allen points out that Google has done very little to market the new service, as most of its users are coming as a product of word-of-mouth. Of course it's still in field-testing mode too. When it opens up to all, it's likely to get a significant boost in new users.
Google also reportedly has a celebrity acquisition plan for Google+. Once it gets a substantial amount of celebrities, users are likely to follow as well. Here is a list of some celebrities that are already using it.
The business crowd will also be a major driving effort for the service. The iPhone app just launched yesterday. That ought to help too.
Page said during the earnings call that Google+ is getting a billion items shared and received in a single day, and that the +1 button is being served 2.3 billion times a day. No stats on how often they're being clicked, unfortunately.