The Office of Research Administration (ORA) requires that all grant applications be received in the office at least FIVE business days prior to the funding agency deadline date.
For example, if an NSF application is due at NSF at 5 p.m. EST on Wednesday, July 8, 2009, it would be due to ORA five business days prior, by 5 p.m. on Tuesday, June 30 (because Friday, July 3 would be a university holiday in observance of Independence Day).National Institutes of Health (NIH)
The National Institutes of Health has three annual funding cycles (Cycle I, II and III) for the most common funding mechanisms. The cycles, whose dates and deadlines vary by mechanism, are each four months long. Current information about the cycles, deadlines, types of programs/mechanisms covered, and other key information is available here.
National Science Foundation (NSF)
The National Science Foundation does not have annual funding cycles but instead has individual due dates for each funding opportunity, which can be updated frequently. Current information about NSF opportunities, submissions and deadlines is available here.
Other funding agencies do not have annual funding cycles, but have individual due dates for each funding opportunity. You will need to check the agency's website to find the submission deadline. Some examples are:

