Answer:
You can apply for Medicare 3 months prior to your 65th birthday, the month of your birthday, and 3 months following your 65th birthday.
Check out this page for information on Medicare:
http://www.medicare.gov/Publications/Pubs/pdf/10050.pdf
You should also know that the 2011 Medicare open enrollment dates are quite a bit different than in 2010. (This is the period when you can switch from Original Medicare to Medicare Advantage and vice versa ... or switch between Medicare Advantage plans.)