While it's difficult to estimate your number of searches, Google Web History shows the total number of searches performed when you were logged in. The service was launched in April 2005, but my account shows data from December 2005.
Google Web History is enabled by default when you create a Google account and it records your searches, the search results you click on and your browsing history, but the last feature is opt-in.
In 2003, Google tested a counter that displayed the number of searches, but that feature didn't go live. "The counter is displayed at the bottom of Google's home page, and shows both a numeric count and a color bar to represent the frequency of your searching. (...) Beyond being an interesting gimmick, what's the purpose of the counter? Though Google has removed the counter FAQ page, its answer to the question What do I win was the zen-like There is no winning. There is only self-awareness. The search is endless."