Ol' Blue Eyes could pick out good songs, but just as important to his success was that he realized the importance of the arrangement to the quality of the recording. One of his signature songs, by Cole Porter and written for a 1936 MGM musical, was "I've Got You Under My Skin." This was a concert standard and owed its popularity as much to Nelson Riddle's huge, swinging arrangement as to Sinatra. You're probably too young to remember this as a top ten hit for the Four Seasons in 1966. Sinatra always recorded live with the band, never singing to a pre-recorded soundtrack.
I, too, discovered "Lost in the Stars" not that long ago. Kurt Weill, another European Jew fleeing the Nazis, was not an active composer in the States for very long, but he left some good ones. Judy Garland's recording of "It Never Was You" is a heart wrencher. I guess Weill is best known for "Mack the Knife," but you would never recognize the original from Bobby Darin's swinging take, one-of-the-all-time-most- played recordings.
I first heard Sinatra singing "Ol' Man River" in the MGM 1946 biopic on the life of Jerome Kern. It was the last and climactic Kern song in the film. I was appalled that this skinny white boy would attempt to interpret the song with the most gravitas in American theater, a song that was always sung by barrel-chested black tenors.
But in a 1963 television special, the second of The Man and his Music specials, he sang it a whole lot differently and it had to at least be taken seriously. That special, available on DVD also features a medley of songs with Antonio Carlos Jobim and the greatest version of "The Lady is a Tramp" ever recorded, a swinging duet with Ella Fitzgerald accompanied by the Count Basie Orchestra.
Getting back to the original question, another candidate for a favorite song, everyone's favorite Sinatra song, is "Just the Way You Look Tonight," written for the 1936 Astaire/Rogers film Swing Time and introduced by Astaire. It won the best song Emmy when this category had a lot more competition. According to Wikopedia, in 2004 it was ranked 43rd out of the top 100 film songs by AFI. I think the legions who have covered it would have ranked it higher. You may remember Rod Stewart's success with it in 2002. He sang it well. The Sinatra version, however, relying on his reliance on arrangers, was done as light swing instead of ballad, and that has made it stand out.
A link to Wikopedia if you want to get an idea of how popular this song has been through the years.
http://en.wikipedia.org/wiki/The_Way_You_Look_Tonight
Curiously, both Rebecca Luker and Kelli O'Hara in separate interviews not long ago named Kern as their favority composer.
