Although OTRCAT.com does not have recordings of every series listed below, the following is quick reference guide to old time radio show series, theme music title, and composer (when available).
Family Hour, The - "Clair de Lune" [from the "Suite Bergamasque"] - Claude Achille Debussy
Famous First Facts (with Joseph Nathan Kane) - "Southearted Men" [from the 1927 musical "New Moon"] - Sigmund Romberg
Famous Jury Trials - "Ase's Death", from the "Peer Gynt Suite" - Edvard Grieg
Fat Man, The - "Fat Man Polka" - Bernard ["Bernie"] Green (psuedonym of Bernard Greenwald)
Father Knows Best - "Father Knows Best Theme" [vocal title: "Waiting"] - Don Ferris (m); Irving Friedman (m); Leon Pober (w)
Fausto Curbelo [big band shows] - Signature Theme on various shows: "Thrill Of A New Romance, The" (1939) - Fausto Curbelo (m); Xavier Cugat (m); Harold Adamson (w)
"Double Concerto, Theme from the" -[2nd Movement Theme from the "Concerto in A Minor, Opus 102, for Violin, Cello and Orchestra"] - Johannes Brahms (m); Cy Feuer (arranger)
Ford's Sunday Evening Hour Of Classics - "Evening Prayer" [Abendsegen, aka "Children's Prayer"], from the opera "Hansel and Gretel" - Engelbert Humperdinck
"La Hoolah Boola [Hawaiian Ditty] (1897) (aka: "Yale Boola" (1901) and "Boola Boola") - Robert ["Bob"] Cole; William ["Billy"] Johnson
"Yale Boola March and Two-Step" (1901) [original title: "La Hoola Boola" (1897)] - Robert ["Bob"] Cole; William ["Billy"] Johnson; with new lyrics by A. M. Hirsh
"Frank Merriwell Theme" - John Winters
Frank Morgan Show, The- "Man That Broke The Bank At Monte Carlo, The (1892)" - Fred Gilbert
[signature song on various programs] - "Night and Day" - Cole Porter
"This Love of Mine" Frank Sinatra; Henry W. ("Hank") Sanicola; Barry Parker
"Put Your Dreams Away (For Another Day)" (1942) Stephan Weiss (m); Paul Mann (m); Ruth Lowe (w)
Frankie Carle [orchestra shows] - Signature Theme on various shows: "Sunrise Serenade" - Frankie (m) Carle (pseudonym of Francis Nunzio Carlone); Jack Lawrence (w)
Frankie Masters [big band shows]
Signature Theme 1 on various shows: "Moonlight and You" - Al Dubin; Kahn Keene; Frankie Masters
Signature Theme 2 on various shows: "Scatterbrain" - Frankie Masters; Johnny Burke; Kahn Keene; Carl Bean