Those of you that have shaky hands when it comes to recording a video need not worry anymore. Google has the solution for you. Google Photos app has recently be updated to help stabilize shaky videos. Android Police reported of a placeholder in the Photos APK last August which has been replaced with a true video stabilization. This allows the app to take a previously recorded video and remove as much shake from the video as possible.
A video comparison was released by Mashable to show you a side-by-side comparison of a video with, and without Photos stabilization which you can view here. A good feature that Google implemented is that, the video that goes through the Photos stabilization does not overwrite the photo, it duplicates the video and stabilizes the duplicated video giving you the option to have both videos kept.
To stabilize a video, you need to download the latest version of Google Photos. From there open up a video you wish to stabilize and tap the pencil icon, select the "Stabilize" option and a progress bar will appear. This new feature has only been implemented for Android phones and is unknown if Google plans to bring it to iOS.