In addition to the three songs mentioned in the previous post, here is a by no means complete list of songs that have been stolen by Jewish performers from secular sources.
"Turkish Kiss" by Tarkan was taken by Piamenta and released as Kol Hamesameach on their album "Big Time."
"Close Every Door" by Andrew Lloyd Webber --from the musical "Joseph and the Amazing Technicolor Dreamcoat" was taken by MBD and recorded as a Yiddish tune about Shabbos. I can't remember the song/album name, but it included the Yiddish lyric "Vi voil is ehr, der Shabbos hiter..."
I haven't included bands such as Shlock Rock here because they acknowledge their use of secular material and don't pretend that it is original.
An example of the way I’d like to see the use of a secular song credited can be found on “The Next Generation’s” album “The Iron Butterfly” whose song “When The Children Sing” is credited as follows: Lyrics by Richard A. Stone/S. Bluth, Music by White Lion. The song uses the music for “When The Children Cry” by the band White Lion.