Here's the list I came up with... it has a few gaps in the 70s and 80s when there was just nothing going on at the Park:
1955 - Any number of movie/TV songs: "Ballad of Davy Crockett," "Whale of a Tale" or "20,000 Leagues Under the Sea," "Merrily on Our Way to Nowhere," "You Can Fly," etc.
1956 - Rainbow Caverns music
1957 - Anything from Sleeping Beauty for the Castle Walk-Thru
1958 - "Alice in Wonderland" or sea shanty from Sailing Ship Columbia
1959 - Monorail Song
1960 - Mine Train Song
1961 - "Disneyland '61" from television show
1962 - Swisskapolka
1963 - "The Tiki, Tiki, Tiki Room"
1964 - From World's Fair: "Get the Feel of the Wheel of a Ford," "There's a Great Big Beautiful Tomorrow," "it's a small world," or "Battle Hymn of the Republic"
1965 - "Battle Hymn of the Republic"
1966 - "it's a small world"
1967 - "Yo Ho (A Pirate's Life for Me)," "Go Go Goodyear," "Miracles from Molecules," or "There's a Great Big Beautiful Tomorrow"
1968 -
1969 - "Grim Grinning Ghosts"
1970 - Show Me America parade
1971 -
1972 - "Bear Band Serenade"
1973 -
1974 - America Sings Introduction
1975 - America on Parade
1976 -
1977 - Space Mountain Atmosphere Queue Music/SFX
1978 -
1979 - "Legend of Thunder Mountain"
1980 - "Disneyland Family Reunion Parade" theme or "Once Upon a Time in Anaheim" (Danny Kaye)
1981 -
1982 - Superspeed tunnel Tron Lightcycles SFX
1983 - "When You Wish Upon a Star"
1984 - "Magic Journeys"
1985 -
1986 - "The Great Outdoors," "Another Part of Me," or "We are Here to Change the World"
1987 - Star Tours instrumental
1988 - Blast to the Past parade
1989 - "Zip-A-Dee-Doo-Dah," "How Do You Do," or "One Man's Dream"
1990 - Party Gras
1991 - Disney Afternoon theme or Celebration U.S.A. parade
1992 - Fantasmic! theme
1993 - Mickey's Toontown theme song
1994 - "I Just Can't Wait to be King," "Circle of Life," or something from Roger Rabbit's Car Toon Spin
1995 - Indiana Jones Adventure onboard music,
1996 - Dick Dale Space Mountain music or Festival of Fools theme music
1997 - "Light Magic," "Zero to Hero" or "it's a small world," holiday music
1998 - "Great Big World of Innoventions," "Magic Highways of Tomorrow," The Mulan Parade or Imagination Institute theme music
1999 - Tarzan's Treehouse music
2000 - "45 Years of Magic Parade" or "Believe... There's Magic in the Stars" soundtrack
2001 - Haunted Mansion Holiday or Holiday Believe
-Jason