An app named Tubemate (which is the most famous app for downloading youtube videos on Android platform) gives you the option to browse youtube's native mobile website and play any video in low quality which I've tested myself. To my surprise, once the loading was done, the video played really smoothly without any buffering. Yes, the quality was really low, but given my internet speed of 5 kbps at that place, I can't complain. Can I?
Btw, the app lets you sign into your youtube account and view and download playlists you've already saved. Basically, because it's the exact mobile website that's loaded, you can do everything you can do using the youtube app on your phone (Don't know if it lets you upload videos). You get an option to download the video in multi resolutions, including HD if available. Also, the video can downloaded as a mp3 file if you just want the sound, like in a video song.
The app is no longer available in the market because it's against Youtube's terms to download their videos. You can download it from any of the links provided on the official Tubemate website.
You can share any app you find really useful in the comments below which shall considered to be included in an App Roundup I'm planning to publish soon. Leave your feedback about the app below.
Have a nice day.