And this year, my wife and I--both of us being essentially freelancers--will be filing quarterly estimated taxes. It's the first year we've really needed to do it, now that we're (A) no longer full-time employees and (B) actually making enough annual income that it matters (i.e., no longer just living off our savings--which, BTW, is a weird loophole in pretty much all US finance regulation, but that's another story).
Chances are you've never cared about estimated taxes, because you're a W-2 wage earner whose paycheck includes automatic withholdings for various taxes (Social Security, Medicare, etc.). Well, when you're a freelancer, those things don't get automatically withheld when clients or customers pay you, but the IRS wants their money all the same. And, as Scalzi says in his excellent "Unasked-For Advice to New Writers About Money" blog post, "the government quite sensibly doesn't trust freelancers to pay their taxes in one lump sum."
So how does it work? Well, I'm sure not qualified to explain it to you, so I'll let my friend Nicole tell you in her well-researched "Surefire Tax Estimating Process for Freelancers" article on The Billfold. And after you absorb all that great information, follow up with The Billfold's other articles on estimated taxes.
It's not actually that much more work, especially since the system is designed to make it easy for you to plan for the coming year when you file your previous year's tax returns; though it's "quarterly," the first deadline of the year is actually April 15th, the same as your federal and state returns. So you can do all the math in one fell swoop, which is what my wife and I did this week. (It helps that she actually enjoys doing taxes, and we live in Washington state, which doesn't collect state income tax.)
Finally, the Treasury Department offers an Electronic Federal Tax Payment System (EFTPS) which lets you pay your taxes online without going through a fee-charging third-party payment service. And for more info on estimated taxes from the horse's mouth, see the IRS's Estimated Tax FAQs and Publication 505: Tax Withholding and Estimated Tax.