According to cofounder Biz Stone, who spoke yesterday at the Aspen Ideas Festival, Twitter now reaches some 800 million search queries per day. That's over 24 billion searches per month, more than Bing (4.1 billion) and Yahoo (9.4 billion) combined.
While Stone's company is still a long way off from Google, which supports around 88 billion search queries per month, Twitter is quickly catching up. Since last April, Twitter searches are up 33%. To put that in perspective, a study by Nielsen last year concluded that Bing was the fastest-growing search engine in the U.S. after it ballooned over 22%. Now it seems Twitter has taken the title. - from here.
The digits are true of course, but as seems to me most of the requests are coming from applications that use Search API. Look for our own projects for example: Checkin, food from Twitter, London on Twitter etc. - all this technically is Twitter Search.