According to this answer, there have been no instances of video recorded from beyond lunar orbit. Mostly, this makes sense as rovers and spacecraft are served just as well with pictures and nothing really moves fast enough to merit taking video (at least I assume that's the rationale). Additionally, spacecraft bandwidth and storage are at a premium and sending a video would be costly.
This changes with NASA's Mars 2020 rover. Seeing the Mars helicopter fly around and preform its mission objectives would be interesting from both an entertainment and scientific/engineering point of view.
- Does the Mars 2020 rover have the capability to record video and will it record the Mars Helicopters' flight to send back to Earth?
- Will the Mars 2020 helicopter record video from its perspective and will this be transmitted back to the rover and then Earth?
Note: I'm defining video as a series of images recorded at faster than 24 fps. Everything slower than 24 fps is a considered a timelapse.