YouTube v4.0.8E with 720p HD playback (WiFi + 3G) (Android) | 3.9MB Mirrors:Letitbit | Rapidgator | Turbobit
The latest version of the official YouTube app.
Keep up with your favorite YouTube channels and access the world’s videos anywhere with the official YouTube app for Android. Requirements: Android 3.2+ (HC/ICS/JB)
How I installed it:
Removed /system/app/YouTube.apk (you need a rooted device for this step! If your device is not rooted, try ignoring this step, but installation may not possible.)
If YouTube is still there, just go into its app info tab and tap "Remove installed updates" or something, then "Force stop".
Install my APK!
Of course, your device must be capable of 720p video decoding!