On Windows, I use ShareX[1], which is free, open-source, lightweight, and has tons of useful features. I love it!
There used to be an issue with ShareX where, by default, it uploaded screenshots and recordings to free online sharing sites, so that you could quickly share links to your files with others. I am not sure if this is still the case, but if you want to give ShareX a try and don't want your files online, make sure to disable this option.