If an internet television station has around 10,000 hours of video clips in a digital format (such as H.264, MPEG 2, or WebM) then what is the best storage medium to archive them with?

Well a lot depends on how the archive is to be used.

For immediate access to the archive at any time at an acceptable cost you're not going to beat spinning magnetic storage [ie disks] but that's a format with a limited shelf life once you take the disks offline. The best way to use disks as a storage medium is to have a big array of them, prefereably in some kind of highly redundant configuration [raid 1+0 or 5+1 or somesuch] and to keep it runnning and replace disks whenever they fail.

For absolute cheapness of storage with reasonable access then writing it all out to DVDs is likely to be the best solution but since these still degrade over time you would need a regular access/test/rewrite policy to ensure the data integrity is maintained.

Magnetic Tape is still the medium of choice for long term data recovery as it's one of the more reliable long term formats out there [I've just personally recovered data from 15 year old DAT tapes that haven't been stored at all within specification or treated gently or even accessed in that time for example]. Magnetic Tape is also one of the cheaper per-gigabyte long term storage mediums as well.

The final viable option that springs to mind is SSD/Flash based storage, has the advantages of being fast and I suspect that if stored properly it's also reliable [but I have no data to back this up at present] but it is also quite expensive for large scale storage arrays.

HTH

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Jake Greenland, CEng MIET.
CCIE #22595

Many thanks for this advice.