The IRS has not yet announced the date that they will start accepting e-filed returns for tax year 2012 yet. Typically it's around the middle of January but the exact date varies from year to year.
I'm putting my money on January 15th with the first round of direct deposits scheduled to go out around January 24th or 25th. That is just an educated guess, however.
You can file a paper return at any time after January 1st once the forms have been released and you have all of your source documents in hand, however the IRS will not start processing those until the day that they start accepting e-filed returns. Since it takes longer to process paper returns you generally will have any refund in hand sooner if you wait for the first day and e-file then and opt for direct deposit.