There were more tweets per day in January 2010 than in the whole of September 2008

"According to our research, Twitter is as of December processing more than one billion tweets per month. January passed 1.2 billion, averaging almost 40 million tweets per day. This is significantly more than Twitter was processing just a few months ago.
[...]
Some interesting observations:
December 2009 was the first month Twitter processed more than one billion tweets (with 1.036 billion tweets).
January 2010 had 16 times as many tweets as January 2009.
The activity on Twitter has doubled since August 2009.
January 2010 saw more tweets per day (39.5 million) than the whole of September 2008."
Source: Pingdom, 10th February 2010
Methodology:
"To be able to calculate the number of tweets per month, we tracked down a tweet from the first couple of minutes of each month. Using the sequence numbers of these tweets, we could then calculate the number of tweets for each month. Since finding old tweets is more or less impossible with Twitter’s own search engine, we used Google, then verified the tweet time stamp by looking at the tweet itself."