Square Facts
Peter Marshall and two contestants in 1967 (left) and on the sport-jacket-loud set used during the show's final year on NBC (right). 
Celebrities on the first NBC show (October 17, 1966) were Nick Adams, Agnes Moorehead, Charley Weaver, Sally Field, Wally Cox, Rose Marie, Morey Amsterdam, Abby Dalton and Ernest Borgnine (who occupied the center square).

Celebrities on the last NBC daytime grid were Rose Marie, Tom Poston, Michelle Lee, Charlie Callas, Vincent Price, Leslie Uggams, George Gobel, Marty Allen, and Wayland Flowers & Madame (center square, since Paul Lynde had left the show).  George Gobel was the last daytime Secret Square but no one picked him during that game.

Rose Marie and announcer Kenny Williams are the only regulars to appear in the first and last episodes
and the pilot; Rose is confirmed as having appeared in the second unaired Sandy Barron-hosted pilot as well.
Future football great, sportscaster and "real killer" searcher O.J. Simpson appeared on the show as a contestant before becoming famous.  He appeared again years later as a Square.  Another future famous contestant: country singer Naomi Judd.
A couple of rare behind the scenes pictures from a 50th anniversary coffee-table book NBC published in 1976. The tic-tac-toe grid was a 18x18  piece of scaffolding.  It may not look very sturdy,  but it survived an earthquake aftershock in the 1971 that shook the entire studio.  All of the stars left their squares during the quake and the studio was evacuated.  No one was hurt but a few studio lights were reportedly damaged.  Joan Rivers (who was there that day) retold that story years later on a talk show, about how Lynde appeared to be the perfect model of composure...until she saw him in the NBC commissary later that day.  Rivers described Lynde as nervously fumbling for change at a candy machine...then looking at her and saying, "I'm so young to go!"
Among the show's many Emmys: five for host Peter Marshall, two for Paul Lynde, and four for the show itself (with producers Merrill Heatter and Bob Quigley accepting).  One of those four was for its last year on NBC, when it tied with The $20,000 Pyramid for Outstanding Game Show.
Frequent Squares guest Joan Rivers directed Billy Crystal in the 1978 bomb "Rabbit Test", in which Crystal plays the world's first pregnant man.  (They never satisfactorily explained how it happened.)  Anyway, The Hollywood Squares heavily influenced this film: Crystal's ob-gyn was played by the Center Square himself, Paul Lynde; George Gobel played a corrupt, Southern U.S. President; and Peter Marshall himself appeared on the HS set.  He explained to viewers that because we now know a man can get pregnant, they've had to recall 522 contestants, bankrupting the show.  So he tearfully says goodbye from the producers, the network, the makers of Ragu Spaghetti Sauce, and Dicker and Dicker of Beverly Hills, as the lights flash on the now-empty grid.  Why the heavy Squares influence?  It could have something to do with the fact that Rivers co-wrote the screenplay with Jay Redack, who was a producer on HS.   (Incidentally, Oscar the Grouch actually plugs "Rabbit Test" in one of the HS episodes on the trading circuit.)
Three in a square: Nine squares didn't always equal nine celebrities.  Sometimes there  were plural squares.  Bill & Susan Seaforth Hayes (Days of Our Lives), pop duo England Dan and John Ford Coley, and even Fred Flintstone and Barney Rubble are among the notable duos who appeared in the same square. All four Lennon Sisters appeared (two each in two squares).  There was a lot of doubling up during theme weeks (devoted to shows like Eight is Enough and Dallas).  In addition, three of the Monkees (Micky Dolenz, Davy Jones, Michael Nesmith) crammed behind one desk in December 1969, and the Hudson Brothers comedy trio did the same in the mid 1970s. 
Speaking of rock groups crammed into a single grid: the New Wave group The Tubes did just that on the back of their 1979 album, "Remote Control."  The group is known for its pop culture satire and the members were reportedly big fans of the Squares, and posed on the set.. The front of that album shows a baby being stared down by an eye-like TV monitor that just happens to be showing...guess what?  The grid from The Hollywood Squares.  And yes, they did appear on the actual show once, on a nighttime syndicated show. 
Where did they sit?  Paul Lynde was center square of course...with Charley Weaver in the lower left, Wally Cox in the upper left and Rose Marie usually in the upper center.  George Gobel perhaps did the most moving.  He was bottom right when he first joined as a regular; when Charley Weaver died Gobel moved to bottom left.
The 1979 fan magazine,  "The Hollywood Squares Contest and Quiz Book,"  gives the following statistics for the show's NBC daytime run up to that point:
Number of questions: 145,000
Hours of programming: 3200
Days of taping: more than 600
Meals to cast and crew: 60,000
Celebrity appearances: 27,000
Prizes given away: $9,000,000  
A game of Musical Squares:  During its combined 15-year run, The Hollywood Squares had three different theme songs.  The main one most of us remember and love--the one with the wild keyboard solo--came from the man you see here, William Loose (The Donna Reed Show and Dennis the Menace), and was used from 1970 to '79.  It's often referred to as "Bob and Merril's Theme", in honor of the two executive producers, Merrill Heatter and Bob Quigley.  The first version, often called "The Silly Song," was performed by the Jimmy Haskell Orchestra, and sounded like a cross between big band and Dixieland.  The third and final version (1979-81) was done by Stan Worth, who also did High Rollers and a few other game show themes.
Calendar Squares

In the process of compiling the celebrity list, Brendan (Beat Master1) found the following dates of interest:

May 29, 1967: The air date of the episode which is available in kinescope form among traders (Joanne Dru, Eva Gabor, etc.), the oldest broadcast episode that has been publicly available.

April 20, 1970: The week that was featured in the
1970 TV Guide article (Linda Cristal, Lohman & Barkley, etc.)

November 23, 1970: The week that features Burt Reynolds, Kathy Garver, etc. whose picture has appeared in many game show books.

October 25, 1971: The week with Frank Gorshin, James Brolin, etc. during which they took a picture of Peter in front of the grid.

May 8, 1972: The first week that Charley Weaver missed because of his heart attack.

January 29, 1973: Charley's first week back.

March 5, 1973: The first week that aired without Wally Cox.

October 22, 1973: The week with Norman Fell, Demond Wilson, etc. whose picture appeared in an Entertainment Weekly retro page a few years back.

July 8, 1974: The week that the
1,000th episode aired (Kent McCord, Ruta Lee, etc.)

July 22, 1974: The week pictured on the "Zingers" album cover (Leslie Uggams, Totie Fields, etc.)

September 30, 1974:  Air date of first week taped after Charley Weaver's death. 

October 7, 1974: The week that is pictured in the
1975 TV Guide article (Richard Crenna, Charo, etc.)

October 27, 1975: Another week whose picture is in many TV books (Douglas Fairbanks Jr., David Brenner, etc.)

Bob Monkhouse, host of the British version of HS (
Celebrity Squares), made an appearance in July of 1975.

The weeks of August 9, 1976 and August 30, 1976 were Storybook weeks, and there were two Storybook shows that aired on the nighttime version in 1977.  The weeks of July 4, 1977,  August 22, 1977, December 19, 1977 and December 26, 1977 also  featured the celebs dressed as figures from history or literature (likely more "Storybook" weeks; the one that popped up on GSN is from the week of December 19).  The three so-called "Party Episodes" making the rounds on the trading circuit were nighttime episodes taped on April 17, 1978 and aired the following month.

Some more dates I found:

April 21, 1965: shooting date for the Bert Parks pilot at CBS Television City in Hollywood.

October 24, 1966: Paul Lynde's first appearance on the show ever, also the show's second week. 

February 26, 1968: Legend has it that during the taping of this week's shows, Jack Palance fell asleep in his square and Michael Landon had to wake him up, all with tape still rolling.

May 27, 1968: This may not be Paul Lynde's first appearance in the center square, but it's the earliest recorded instance I have.

July 8, 1968: Week that Eartha Kitt taped before her infamous anti-Vietnam speech at the White House, but it aired afterwards; ensuing controversy led to her never appearing on the Marshall
Squares again.

February 8, 1971: The one and only appearance by the one and only Groucho Marx.  It seemed like a naturally good idea but Marshall recalls Marx being a disaster, and even appearing to agree with it afterwards.

December 10, 1973: George Gobel's earliest recorded appearance on the NBC version.

March 23, 1974: Week in the photo that's on the cover of Peter Marshall's book,
Backstage With the Original Hollywood Square (Kent McCord, Art Linkletter, etc; not pictured is Demond Wilson) 

November 3, 1975: a tenth-season kickoff week in which the show experiments with an hour long format like
The Price is Right.    Highlights: rarely shown clips of the 1965 pilot, Milton Berle losing his patience with the irritating laugh of a contestant, and Art James tartly corrects Peter Marshall's pronunciation of "Sacajawea."

August 15, 1977: Andy Kaufman appears; angry letters from viewers who thought he was disrespecting Peter Marshall resulted in Kaufman not being invited back.  (Marshall was actually not offended and in fact thought Kaufman was very funny.)  Ironically, Elvis Presley died that week, and Kaufman is well remembered for imitating Elvis in his act.

June 19, 1978: the week of the 3,000th show, with guests including Marsha Mason, Eileen Brennan and Louise Fletcher (as seen in the anniversary photo) and other cast members from the movie "The Cheap Detective."

November 27, 1978: a week of soap stars.

December 4, 1978: the
Barney Miller cast week.

May 17, 1979: the youngest collection of squares ever. (Adam Rich, Dana Plato, etc.) 

July 2, 1979: a second week of soap stars.

July 23, 1979: the
Dallas week.

July 30, 1979: During this week, Melissa Gilbert appears with siblings Jonathan and four-year-old Sara.

August 20, 1979: Paul Lynde's last appearance on the NBC daytime version.

November 19, 1979: Week that Hugh Downs appeared.  He was anchoring
20/20 at the time, making him the only working newsman to ever appear in a square.

December 3, 1979: yet another soap week.

January 14, 1980: A "rotating squares" week with standup comics (Elayne Boosler, Gallagher, etc.)

March 24, 1980: A country week, possibly even tied to
Hee Haw.
Unlikely Squares

Celebrities you might not have known were on the Marshall Squares

Hank Aaron
Milton Berle
Elayne Boosler
Ernest Borgnine (the first center square)
Beau Bridges
James Brolin
Mel Brooks
George Carlin
Billy Carter, "first brother"
Ray Charles
the Commodores (including Lionel Richie)
Alice Cooper  (yes, the rock star)
Billy Crystal
Jamie Lee Curtis
Sammy Davis Jr.
Hugh Downs (while he was
"Mama Cass" Elliot
Sally Field
George Foreman
Teri Garr
Marvin Gaye
Sara Gilbert (age 4)
Betty Grable
Pam Greer
Janet Guthrie (pioneering race car driver)
Gene Hackman
Bob Hope
Ron Howard
Naomi Judd (contestant)
K.C.  (of the Sunshine Band)
Bob "Captain Kangaroo" Keeshan
Andy Kaufman
Chaka Khan

Dorothy Lamour
Gypsy Rose Lee
Janet Leigh
Jay Leno
David Letterman
Mickey Mantle
the Marshall Tucker Band
Steve Martin
Groucho Marx
Walter Matthau
Tug McGraw
three of the Monkees
Roger Moore
Leonard Nimoy
a sleepy Jack Palance
Floyd Patterson
Vincent Price
Rob Reiner
Burt Reynolds
Jane Russell
George C. Scott and his wife,
  Trish Van Devere
William Shatner
O.J. Simpson
Sonny & Cher
Jacqueline Susann
Gloria Swanson
Margaret Truman (yes, the presidential daughter)
Tanya Tucker
The Tubes
Tina Turner
Abigail "Dear Abby" Van Buren
Vivian Vance
Jack Webb
Adam West
  People who, surprisingly, never appeared on the Marshall Hollywood Squares
Orson Bean
Joyce Bulifant

Carol Burnett
Clifton Davis
Richard Dawson
Richard Deacon
Geoff Edwards
Arlene Francis
Joe Garagiola
Anita Gillette
Elaine Joyce
Allen Ludden
Dick Martin
Jack Narz
Gary Owens
Betsy Palmer
Nipsey Russell
For more Square trivia, click here.

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