I hate it when someone asks me what my favorite song is. There are just way too many wonderful ones.
And, of course, so much depends on your genre preferences.

But among my favorites, especially on the melody side, are:

Greensleeves
Star Dust
O Mio Bambino Caro
Torna A Surriento
Die Lorelei
The Water Is Wide
Yesterday (McCartney)
Granada
Lorena
Over The Rainbow
The Tennessee Waltz
The First Time (Ever) -- the ORIGINAL Ewan McColl tune, not the 'refurbished' tune done by Roberta Flack and everyone since
Blues In The Night
Ode To Joy (Beethoven)



OK, maybe a lot of that is based on familiarity, and I'm probably overlooking a lot of tunes that just don't pop into my mind readily, but I do think those are beautiful melodies.