The announcement of the royal baby generated a peak of >25,300 tweets per minute

"The birth of a baby into a royal family has always generated global interest. It’s no different in our 24/7 era.
So when the Duke and Duchess of Cambridge announced the birth of their first-born today, it was fitting that the team at Clarence House (@ClarenceHouse) quickly turned to Twitter to send out the word to well-wishers everywhere.
The first confirmation that a royal arrival was imminent came at 7:37 a.m. BST this morning when the couple’s official Twitter account @ClarenceHouse tweeted.
The scale of the global conversation was immediately apparent. Since that announcement, there have been more than two million mentions of the news on Twitter, with well-wishers gathering around hashtags including #RoyalBaby, #RoyalBabyBoy and #RoyalBabyWatch.
The peak in conversation on Twitter about the news came at 8:37 p.m. BST in the minutes following the announcement of the baby’s birth, with more than 25,300 Tweets per minute.
As royal-watchers all over came together to share their excitement, the hashtag #RoyalBaby became the gathering place for messages of congratulations. Since the Duchess was admitted to hospital, that hashtag alone has been used more than 900,000 times on Twitter."

Source:  Twitter blog, 22nd July 2013
Update - It also generated 19m posts, likes and comments on Facebook in the UK alone