A lot of discussion of the highest-quality audio file formats here (e.g. lossless AAC). How about video formats? What is the highest-quality video format?

There are no lossless video formats, so you'll have to decide for which format is best for which use case.
For broadcasting you'll want MPEG-2 for SD and MPEG-4 High Profile (H.264) for HD, both in a Transport Stream container.
For distribution to end users, you'll most likely want to use XViD in .mp4 or .avi container for SD and to suit older devices.
If you're short on bandwidth and can sacrifice users with old hardware, or if you're distributing HD material, use H.264/x.264 with .mp4 or .mkv as a container.

It's usually a good idea to follow whatever the Warez Scene or the Porn industry sets as a standard, as that is usually what is followed by consumer electronics.
http://en.wikipedia.org/wiki/Standard_%28warez%29

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