First recorded by Gertrude Lawrence (US #2 1926).
Other hit versions by George Gershwin (US #13 1926), George Olsen & His Orchestra (US #3 1927), Frank Sinatra (UK #13 1954), Linda Ronstadt (1980).
Also recorded by Margaret Whiting (1944).
From the wiki: “‘Someone to Watch Over Me’ was composed by George Gershwin with lyrics by Ira Gershwin for the musical Oh, Kay! (1926). George Gershwin originally approached the song as an uptempo jazz tune, but his brother Ira suggested that it might work much better as a ballad, and George ultimately agreed.