The deadline to file your 2013 income taxes remains 11:59 p.m. April 15, 2014. If you cannot complete your tax paperwork by that time, the IRS will give you an extension to file, but not to pay. The IRS extension to file is automatic if you file the appropriate paperwork, known as Form 4868, by that same deadline less than two weeks from now.
Form 4868 is available at this link; it can be filed electronically or on paper. The extension gives you an additional six months -- until October 15, 2014 -- to complete your paperwork, but you still must pay your 2013 income taxes by April 15, even if you receive that extension.
What if you don't?
If you don't file your taxes or request an extension on time: The IRS will charge a late filing penalty equal to 5% of your tax due for each month (or partial month) you are late to file, up to a 25% total penalty. There's a minimum penalty of $135 (or the total tax amount due, whichever is smaller), which you'll owe on top of any taxes due.
If you don't pay your taxes on time: The IRS will charge you a late payment penalty equal to 0.5% per month of any tax due and not paid by April 15, with a maximum penalty of 25%. Even there, the IRS is somewhat reasonable in that it won't charge you that particular penalty if you pay at least 90% of your total 2013 taxes owed through withholdings, estimated taxes, and/or your form 4868 submission.
In addition, the late payment and late filing penalties can stack on top of one another, to a maximum combined penalty of 47.5%. These penalties are added to both the taxes you owe and the interest you owe for not making the payments in a timely manner.
What are you waiting for?
There are some legitimate reasons why you may not have filed your taxes yet. If you haven't, you're not alone.
If you lived outside of the United States in 2013, the paperwork can get incredibly complicated and may take additional time to get right. Similarly, if you've recently moved, and not everybody involved in your taxes has your updated address, you may not have all the paperwork needed to complete your filing on time. Likewise, you may be a bit behind the filing curve if you've faced a disaster like a fire, a tornado, or a death in the family.
On top of those reasons, certain investments, such as partnerships, don't technically have to file their tax paperwork until April 15, 2014. If you're a partner in a partnership that doesn't submit its paperwork until that date, you may simply not have all the materials necessary to complete your own tax return on time.
Whatever your reason, the IRS doesn't care if you miss the April 15 deadline to file your 2013 taxes, so long as you file for the extension and pay what you owe for last year by that date. So if you can't get your tax paperwork completed on time, at least finish form 4868 by then to get your automatic extension and ward off those late-filing penalties.