I have made various end of year business purchases with a credit card. Do I get to claim those as expenses for this year (2009), when I used the card? Or if I don't actually pay off the card until the bill comes in January, are they expenses for next year (2010)?

Expense them when you buy them. A credit card is revolving credit and just like a loan. And you do it that way every year, not just this one cause you apparently want to count the expenses.