Actually, there
are quite a few pre-1972 shows that exist, although almost none of them circulate:
* A test episode taped March 5, 1964, held by Paley Center. The Trebek version used a brief clip on their 4,000th show.
* The first five minutes of the September 7, 1966 show (#638, Libby Dyer/Joy Johnson/Irene Brody) exist as a master copy with slate, albeit in B&W with average quality.
* Three episodes of the National College Scholarship Contest from 1967 (816, 818, and 819) are held by UCLA. #819 was the Finals, a clip of which appeared in the 1975 finale.
* Archival Television Audio, Inc. has two episodes from 1968: May 31 (with David Canary of
Bonanza making an appearance), and August 6. They also have an October 1974 show.
* Dr. Burt Sherman's five games (August 1968), along with his appearance in the 1969 Tournament of Champions (#1435), all exist in audio form. They were recorded by his family, along with some 8mm home movie clips (mostly of Day 5).
* UCLA has five episodes from 1971: March 8, March 16, March 24, April 1, and April 9. They also have five shows from March-April 1973.
* The 1975 finale also had a clip of Gene Shalit getting an Audio Daily Double, although I'm not sure when that was.
Eric noted the others, although they really only amount to the 2,000th show, two shows from 1974, and the '75 finale. As such...
My sister-in-law wanted me to find out if there were any Jeopardy! episodes from 1967 because a friend of her's mother passed on recently, and she was on Jeopardy! [...] Could anyone let me know about the status of the Flemming J! episodes and if NBC might happen to have any?
I don't think NBC has any episodes -- they and/or Merv seem to have junked nearly all of them. It's possible that the only remaining record of her game(s) is in the microfilm archives NBC donated to the Library of Congress, although even that's uncertain.