What are those melodies, from classical music, that ALL PEOPLE recognize?
The following come to my mind...
-Beethoven "Fur Elise"
-Beethoven opening motif of the 5° symphony
-Beethoven "Ode to Joy" from his 9° symphony
-Bach-Petzold "Minuet in G major"
-Bach "Tocatta and Fugue in D minor"
-Tchaicovsky opening motif of his "1° Piano Concerto"
-Ravel "Bolero"
-Mozart "40° symphony (1° movement)"
-Mozart "Sonata K331, 3° movement" (Rondo a la Turca)
Add your candidates !! I am sure there are a lot more !!
Keep in mind that candidates should be recognized by at least 90 % of people, with or without musical background !!
PD: i do not think any Chopin work fall into this "absolutely popular" category. What do you think? His "Heroique" Polonaise is the closest candidate, IMO.