For years YouTube's built-in editor has included a tool for blurring faces and objects in your videos. The editor has two blurring options. The first option is "automatic face blurring" which automatically detects faces and blurs them. The downside to using that option is that it will blur all faces for the whole length of the video. That's fine unless you want to selectively blur faces or you want to blur something besides a face. The other blurring option in the YouTube editor is to selectively blur. That option lets you manually place a blurry box or oval over a section of your video. Both blurring options are demonstrated in this short video.
Screencastify's recently updated free video editor also offers an easy way to blur faces and objects in your videos. In Screencastify's video editor you can choose to blur any face or object for as long as you like in your videos. You can also have multiple blurs running simultaneously in your video. Screencastify's object blurring feature is demonstrated in this video.