Assuming you've got simple taxes (you don't work for yourself, didn't pull from your retirement, etc. You'll probably know it if you have "complex" taxes) and live in the USA, Free Tax USA will let you file free federal and has the cheapest state filing I've found. They're also a fairly trustworthy company that's not owned by Intuit and their corporate allies, so that's a plus.
EDIT: Adjusted the level of trustworthiness.
I've used Free Tax USA in the past, but I wouldn't say they're trustworthy. They're still part of the free file alliance and actively lobby against the IRS creating their own free tool without any restrictions.
Better than Intuit, at any rate. FTUSA have never let me get all the way through my taxes before springing on me that I need to buy their extra services, despite the fact that their free edition is supposed to cover the thing, then you find out that their widely available "free edition" is designed to route you to their paid services and that the actually free free edition is located on a totally different website and... Yeah, looking at you, TurboTax.
Federal, and you don't have any especially unusual sources of income? Just use https://www.freefilefillableforms.com/ directly from the IRS.
