USCIS started accepting applications for H1b on April 1, 2011 for the Fiscal Year 2012. The actual start on the H1b applications will be October 1, 2011 or later.
Today, USCIS released the first set on the number of applications they received. As of April 7, 2011. They have received 5,900 applications towards the 65,000 maximum regular H1b quota and 4,500 applications towards the 20,000 maximum advanced degree h1b quota.
More details: http://www.uscis.gov/h-1b_count