Google Searches today
Google now processes over 40,000 search queries every second on average (visualize them here), which translates to over 3.5 billion searches per day and 1.2 trillion searches per year worldwide. The chart below shows the number of searches per year throughout Google's history:
When Google was founded in September 1998, it was serving ten thousand search queries per day  (by the end of 2006 that same amount would be served in a single second). In September 1999, one year after being launched, Google was already answering 3.5 million search queries daily. 
Nine months later and, in mid 2000, search volume had increased fivefold, reaching 18 million queries on an average day.  By the time Google announced its IPO in April 2004, users around the world were submitting more than 200 million queries to Google every day.
In August 2012, Amit Singhal, Senior Vice President at Google and responsible for the development of Google Search, disclosed that Google's search engine found more than 30 trillion unique URLs on the Web, crawls 20 billion sites a day, and processes 100 billion searches every month  (which translate to 3.3 billion searches per day and over 38,000 thousand per second).
After expanding significantly in the first decade of the 21st century, Google's search volume growth rate started to decline in 2009 and 2010, and is currently estimated to be at around 10% per year.
In the start-up phase growth was phenomenal, with a 17,000% year to year increase in search volume between 1998 and 1999, 1000% between 1999 and 2000, and 200% between 2000 and 2001. Google search continued to grow at rates of between 40% to 60% between 2001 and 2009, when it started to slow down stabilizing at a 10% to 15% rate in recent years.
Baidu has a 8.2% share (14.5 billion searches in December 2012).
Yahoo 4.9% (8.6 billions searches in December 2012).
Yandex 2.8% (4.8 billions searches December 2012).
Microsoft sites (mostly Bing) 2.5% (4.5 billions searches December 2012).
Even though as Yandex and Baidu might be growing at a somewhat faster rate compared to Google, the distance between Google and the other search engines in terms of search volume is so vast that any moderate growth differential doesn't impact Google's global leadership in any significant way (see chart below).