Audacity ( is a free audio recording and editing software program that can do some amazing things for the price:). We even have a tutorial course with videos showing you how to begin audio recording with almost no budget by using audacity - The Newbies Guide To Audio Recording Awesomeness 1: the Basics With Audacity.
It has always had a noise reduction tool - called "Noise Removal" - that worked fairly well. But frankly, though it was OK in a pinch, it wasn't really very good.
But with the release of version 2.1 in July, 2015, they upgraded the tool - now called "Noise Reduction." And it works a lot better than the original version!
Below is a video demo of the new Noise Reduction tool in Audacity 2.1 (and later). I just did a quick voice recording with the air conditioning running in the room, which causes a steady, low frequency background noise. Judge for yourself:). You can hear the noise (and then lack of it) better if you wear headphones.
If you use Reaper, here is how to do noise reduction using their built-in tools: ReaFIR Madness – The Hidden Noise Reduction Tool in Reaper