Is there any space agency that provides a live video of Earth, in HD? Preferably without anything man-made in the way (e.g some ISS robotic arm)?
I want to create a live HD wallpaper of Earth, so I'm looking for a good source for that.
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As far as I know, only NASA (since you asked for the agency) through its High Definition Earth Viewing (HDEV) Experiment gives the live coverage of the Earth from the ISS. It might not be up for all the time and they sometimes switch to previously recorded videos in case of technical problems but this is only source I know available in the public domain.
During "loss of signal" periods, viewers will see a blue screen. Since the station orbits the Earth once every 90 minutes, it experiences a sunrise or a sunset about every 45 minutes. When the station is in darkness, external camera video may appear black, but can sometimes provide spectacular views of lightning or city lights below.
It could be watched either on YouTube or Ustream (as advertised on the NASA page). My preferred way is ISS Live Now app (look for Camera HD). There are couple of caveats though, one is the footage might not be that sharp to be used as wallpaper. Also, sometimes you might see the visiting spacecrafts docked to the station (Soyuz, Dragon, Cygnus, etc.)
All other sources claiming to give the live view basically points to the same stream. Besides, a quick Google search yielded this website which posts the high resolution satellite pictures in near real time. It also has current location feature which might be useful for your application.
Bonus - I remember once Scott Manley posted a 10 hour long rotating Earth footage constructed using data from the the DSCOVR mission which was stationed at the Langrange point L1 between Earth and the Sun. See him describing the process here. It's pretty cool.