Characteristics of great tunes:

Memorable
Wear like iron
Singable or hummable
You catch yourself humming them at odd times of the day
Unites people in a common cause if accompanied by at least 2 of the above ;-)
etc.

Examples can be found in folk songs of the world, certain patriotic songs
like the ones already mentioned, and in the occasional "classical" work.
I would suggest that "To Anacreon in Heaven" aka Star-spangled Banner is
not a great tune.

In general I find Mozart's tunes more memorable than Haydn's, which I
find more interesting from the standpoint of their humor and potential
for motivic development.  Some of my favorite Mozart tunes include from
Don Giovanni: La ci darem, Batti batti, Deh vieni alla finestra.

Beethoven: Ode to Joy of course but don't forget the second theme from the
Adagio of that same symphony.

Of course the hymn from Finlandia, the center cut from Jupiter (Holst),
Verdi's Chorus of the Hebrew slaves from Nabucco, all have a sort of
universal quality and can stir the blood when appropriate.

Chris Bonds