The table below contains all known Mouseketeer Fun With Music Day musical numbers appearing in the first season of the original Mickey Mouse Club, by order of appearence. If you find that your favorite number doesn't appear here, it might have been on Anything Can Happen Day.
Storyline credits are assumed to be Bill Walsh, Hal Adelquist, Perce Pearce, and Roy Williams. Bob Amsberry should probably be credited for any skit for which he also wrote the song. Song credits are listed in parantheses. Where available, images and video links have been provided from the actual show. For some of the shows there is no picture available. Only original broadcast appearences are listed; reruns are excluded. Note that some musical numbers or photos might be incorrectly assigned to a particular show. While all shows are listed, the songs and other credits for them are incomplete.
Most of the information below was extracted from original research done by Bill Cotter, however, any errors of fact or mistakes in interpretation are my own. Quite a few photos, descriptions, and cast lists come courtesy of Rick from Dallas (RfD).
  Season 1   (1955-56)  

  The Friendly Farmers  
  Oct 3, 1955  
  Lead: Bob Amsberry, Thurl Ravenscroft (voice only) 
  With: Mary Sartori, Lonnie, Bonni, Dennis, Bronson, and Tim  
  Songs: The Friendly Farmers (Amsberry/Baker/Marcellino)  
  It's unfortunate this novelty song and dance was the first Mouseketeer number ever seen. Jack Gould of the New York Times singled it out for derision in his review the next day, which may have caused Walt Disney to bear a grudge against Bob Amsberry.

  The Shoe Song #1  
  Oct 3, 1955  
  Lead: Roy, Jimmie  
  Solo: Bronson, Karen, Darlene, Cubby, Sharon  
  With: Dennis, Bobby, Bonni, Doreen, Mike, Mark, Don  
  Song: The Shoe Song (Jimmie Dodd)  
  This number seemingly began in the middle, with Jimmie giving a voice-over intro.

  The Pussycat Polka  
  Oct 10, 1955  
  Lead: Jimmie Dodd (voiceover), Ruth Carrell (voiceover)  
  With: Billie, Mary Espinosa, Lonnie, Bonni, Nancy, Dallas*  
  Song: Pussycat Polka (Jimmie Dodd)  
  Jimmie and his wife Ruth performed this song in voiceover, while six mice danced in cat costumes. Jimmie's predeliction for cats ran counter to Walt Disney's usual feelings about felines. *According to later recollection by Mary E., this was one of three numbers with Dallas Johann (RfD).

  Old MacDonald #1  
  Oct 10, 1955  
  Lead: Jimmie Dodd, Darlene Gillespie  
  Solo: Bob Amsberry, Dennis, Mary Espinosa, Karen, Cubby, Roy  
  With: Sharon, Doreen, Mike, Mark, Bonni, Don, Bobby, Bronson  
  Song: Old MacDonald (trad., Jimmie Dodd, Roy Williams)  
  Jimmie and the younger kids sing about unconventional animals, while the older kids explain what they are.

  Do-Mi-So  
  Oct 17, 1955  
  Lead: Jimmie, Darlene, Tommy  
  With: Unknown  
  Song: Do-Mi-So (George Bruns)  
  Darlene as Mary, Mary Quite Contrary and Tommy as Little Boy Blue lead three other Mouseketeers in this swinging big-band cross between American folk tunes and Mother Goose.

  I Am Not Now and Never Have Been in Love  
  Oct 17, 1955  
  Lead: Tommy  
  With: Nancy, Darlene, Annette, Doreen  
  Song: I Am Not Now and Never Have Been in Love (Adair/Fine/Penner)  
  (RfD) Tommy helps Nancy up after she falls, and gets teased by other kids offstage. He sings his disclaimer about love, but a dream ballet sequence with the other three girls changes his mind.

  Animals and Clowns  
  Oct 24, 1955  
  Lead: Jimmie  
  With: Billie, Judy, Nancy, Roy, Mary E., Lonnie, Dallas  
  Song: Animals and Clowns (Imogen Carpenter/Lenny Adelson)  
  This songwriting team worked with Judy Harriet on several of her post-MMC films and recordings. Unusual number in that the background vocals were provided by an adult chorus. Dallas is inside the drum, which has a clear plastic front, and his name is clearly visible on his shirt (RfD).

  Old MacDonald Had a Tree #2  
  Oct 24, 1955  
  Lead: Jimmie Dodd, Roy Williams  
  With: Unknown  
  Song: Old MacDonald Had a Tree (trad./Jimmie Dodd/Roy Williams)  
  No information on this

  Old Betsy  
  Oct 31, 1955  
  Lead: Jimmie Dodd  
  With: Nancy, Billie, Judy, Mary E., Lonnie, Dallas  
  Song: Old Betsy (Gil George/George Bruns)  
  'Old Betsy' was the name Davy Crockett gave his rifle. The photo comes from the end of the skit, after Jimmie fires Old Betsy into the sky. (RfD)

  Green Grass Grows All Around #1  
  Oct 31, 1955  
  Lead: Jimmie, Roy  
  Solo: Bobby, Bonni, Don  
  With: Karen, Cubby, Sharon, Darlene, Doreen, Mark, Dennis  
  Song: Green Grass Grows All Around (trad/Jimmie Dodd/Buddy Baker)  
          Irish Washerwoman (trad/arr Buddy Baker)  
  Several of the first season numbers were filmed with alternate lyrics, gags, and even cast members, then shown on different days.

  Sho Jo Ji aka The Hungry Racoon  
  Nov 7, 1955  
  Lead: Ensemble  
  Solo: Billie, Nancy, Mary Espinosa, Mike, Roy, Lonnie, Bobby  
  Song: Sho Jo Ji (trad/Bill Walsh)  
  This one is unlikely to be seen again. Bill Walsh cribbed this from a traditional Japanese kid's song, about an animal called a tanuki.

  Simple Simon #1  
  Nov 7, 1955  
  Lead: Roy Williams  
  Solo: Darlene, Bobby, Bonni, Cubby, Doreen, Bronson, Mark  
  With: Karen, Don, Mike  
  Song: Simple Simon (trad/Jimmie Dodd/Tom Adair)  
  No information on this

  Humphrey Hop  
  Nov 14, 1955  
  Lead: Unknown  
  With: Lonnie, others  
  Song: Humphrey Hop (Dawes Butler/George Bruns)  
  During the filming of this number, the crew reportedly broke for lunch and left the kids trapped in their bear costumes.

  Green Grass Grows All Around #2  
  Nov 14, 1955  
  Lead: Unknown  
  With: Unknown  
  Song: Green Grass Grows All Around (trad/Jimmie Dodd/Buddy Baker)  
  No information on this

  Roy at the Dike aka Boy at the Dike  
  Nov 21, 1955  
  Lead: Roy Williams  
  With: Unknown  
  Song: Roy at the Dike (George Bruns)  
  No information on this

  Painting Aunt Polly's Fence  
  Nov 21, 1955  
  Lead: Jimmie Dodd  
  With: Cubby, Lonnie, others  
  Song: Painting Aunt Polly's Fence (Gil George/Paul Smith)  
  Jimmie, as Tom Sawyer, gets the other boys to pay him for the privilege of white-washing Aunt Polly's fence.

  Mickey Mouse Mambo  
  Nov 28, 1955  
  Lead: Unknown  
  With: Mary Sartori, Johnny, others  
  Song: Mickey Mouse Mambo (No credit available)  
  Not much information on this

  I'm a British Grenadier  
  Nov 28, 1955  
  Lead: Bob Amsberry  
  With: Bronson, Darlene, Lonnie, Doreen, Johnny, Roy  
  Song: I'm a British Grenadier (Bob Amsberry/Muzzy Marcellino)  
  Palace sentry Bob sings while he stands guard. 'Prentice lads and lasses try to make him smile, but it takes an obnoxious tourist (Roy) to accomplish it.

  A Cowboy Needs a Horse  
  Dec 5, 1955  
  Lead: Dennis  
  With: Unknown  
  Song: A Cowboy Needs a Horse (Paul Howard/William Mills)  
  (RfD) This was a "dream sequence" number, with only Dennis visible; the other Mouseketeers were in cactus costumes.

  Simple Simon #2  
  Dec 5, 1955  
  Lead: Roy  
  With: Lonnie and others  
  Song: Simple Simon (trad/Jimmie Dodd/Tom Adair)  
  No information on this

  Get Busy  
  Dec 12, 1955  
  Lead: Unknown  
  With: Bobby, Karen, Cubby, and others  
  Song: Get Busy (Jimmie Dodd/Tom Adair)  
  This seems to have been another game type number, like the What Am I? shows on Anything Can Happen Day. This one evidently involved doing household chores.

  The Shoe Song #2  
  Dec 12, 1955  
  Lead: Jimmie  
  Solo: Nancy, Sharon, Doreen, Darlene, Lonnie, Bobby, Don, Karen  
  With: Annette, Johnny, Mike  
  Song: The Shoe Song (Jimmie Dodd)  
  Thanks to Rick from Dallas for providing information on this

  Be Sure You're Right  
  Dec 19, 1955  
  Lead: Unknown  
  With: Unknown  
  Song: Be Sure You're Right (Fess Parker/Buddy Ebsen)  
  No information on this

  Hi To You  
  Dec 19, 1955  
  Lead: Jimmie, Karen, Johnny  
  With: Bonni and others  
  Song: Hi To You (Dodd/Gyldmark/Skaarup)  
  (RfD) This number was based on a Scandinavian folk song, sung by the leads, with the other mice pretending to skate around an ice pond. A very much sought-after number by collectors, it is almost a lost episode.

  Roy, Roy, Quick on the Draw  
  Dec 26, 1955  
  Lead: Roy Williams, Jimmie Dodd  
  With: Bonni, Dennis, Bronson, Tim, Mary Sartori, Mark, Don, Lonnie  
  Song: Roy, Roy, Quick on the Draw (Bob Amsberry/Muzzy Marcellino)  
  Bad-guy Roy is a quick-draw graffiti artist whose gun has black chalk in the barrel. Jimmie is the sheriff, whose gun holds an eraser.

  Ten Little Indians  
  Dec 26, 1955  
  Lead: Jimmie Dodd, Annette  
  With: Roy, Lonnie, Doreen, others  
  Song: Ten Little Indians (Bob Amsberry/Muzzy Marcellino)  
  (RfD): This had Annette and Jimmie introducing and singing the song in close-up, perhaps an early studio acknowledgement of Annette's fan mail. They also closed the number, which included Roy being "scalped", and Doreen stumbling and nearly falling during the dance.

  Cool, Calm, and Collected  
  Jan 16, 1956  
  Lead: Unknown  
  With: Unknown  
  Song: Cool, Calm, and Collected (Bob Amsberry/Muzzy Marcellino)  
  No information on this

  Cooking with Minnie Mouse  
  Jan 16, 1956  
  Lead: Jimmie Dodd, Ruth Carrell  
  Solo: Bobby, Darlene, Doreen, Annette, Nancy  
  Song: Cooking with Minnie Mouse (Ruth Carrell/Jimmie Dodd)  
  Terrific little number, well-staged by Dik Darley. Burch Mann threw touches of An American in Paris into the choreography. As with so many of these numbers, Buddy Baker's musical arrangements really made the whole thing come alive.

  The Village Blacksmith  
  Jan 23, 1956  
  Lead: Unknown  
  With: Unknown  
  Song: The Village Blacksmith (Gil George/Paul Smith)  
  No information on this

  The Pencil Song  
  Jan 23, 1956  
  Lead: Jimmie Dodd  
  With: Unknown  
  Song: The Pencil Song (Jimmie Dodd)  
  Jimmie Dodd performs the song that both got him hired by Disney and won the job hosting the show.

  When I Grow Up  
  Jan 30, 1956  
  Lead: Darlene Gillespie  
  Song: When I Grow Up (J. Francis Burke/Jimmie Dodd)  
  Darlene's signature song was this sentimental ballad, probably written with her in mind. Her voice had an especially poignant quality in her teenage years.

  Mixed-up Mother Goose  
  Jan 30, 1956  
  Lead: Unknown  
  With: Unknown  
  Song:  
  No information on this

  Mousekedance  
  Feb 6, 1956  
  Lead: Jimmie  
  With: Don, Mary Sartori, Bonni, Bobby, Lonnie, Annette  
  Song: Mousekedance (Jimmie Dodd)  
  Don and Mary get dance help from Jimmie and the other kids.

  Song of the Dance/South  
  Feb 6, 1956  
  Lead: Ensemble  
  With: Johnny, Judy, Darlene, Annette, Doreen, Mike, Sharon, Bobby  
  Song: How Do You Do?  
  The title of this number is in doubt. No other reference to 'Dance' has come my way, but 'South' is proved by photo from RfD, who also provided cast list. No doubt a tie-in to re-release of Song of the South.

  Animal Alphabet  
  Feb 13, 1956  
  Lead: Jimmie Dodd  
  With: Mary Sartori, Darlene, Annette, others  
  Song:  
  No information on this; photo and cast list are only a guess

  Fun with Music  
  Feb 20, 1956  
  Lead: Unknown  
  With: Unknown  
  Song: Fun with Music (M.David/J.Livingston/J.Dodd/Hoffman)  
  This song was superceded for the second season by the Sid Miller/Tom Adair version. Mack David and Jerry Livingston later wrote many TV themes for Warner Brothers (Maverick, 77 Sunset Strip, Hawaiian Eye).

  Mousegetar Music Lesson  
  Feb 20, 1956  
  Lead: Jimmie  
  With: Darlene, Judy, Annette, others  
  Song:  
  (RfD) This was a behind the scenes glimpse of Mouseketeers relaxing; the three girls get a guitar lesson from Jimmie, while other mice do their own thing. Perhaps a commercial tie-in to the licensed marketing of the Mousegetar.

  Hiawatha  
  Feb 27, 1956  
  Lead: Jimmie Dodd  
  With: Annette, Mark, others  
  Song: Hiawatha (Gil George/Jimmie Dodd)  
  No information on this, and not sure photo and cast list belong to this show

  Johnny Appleseed  
  Feb 27, 1956  
  Lead: Jimmie  
  Solo: Cubby, Tommy  
  With: Judy, Annette, Karen, Roy  
  Song: Johnny Appleseed (Ken Darby/Paul Smith)  
  Several brief songs from the Disney animated short make this more like a skit than the usual standalone numbers. Has two things I can't recall elsewhere on MMC: a kiss (Karen to Roy) and a song solo by Cubby.