Videora Android Converter is a free, lightweight video converter. The graphical user interface is entirely made in HTML, which makes it easy for anyone to use the application. There are two conversion modes, one designed for beginners and one for more advanced users. In the first mode, all you need to do is to select the file that you want to convert, specify where you want to save the new file, and then move a few sliders to change the conversion settings. These sliders let you change the format, video size (aspect ratio), video quality, audio quality, and to enhance the video quality. The app will then estimate the speed and quality of the file and its size and display it at the bottom of the screen. If you want to, you can access the "Power mode", which lets you select a conversion profile and removes a few steps from the process. You can edit the conversion profiles from the settings window.
This app comes packaged with YouTube Downloader App, which should let you download videos from YouTube. Then you can use the converter to make sure those can be played on your Android device. Unfortunately, I was unable to get the downloader to work at all.