There's a band in my country that had a hit single, then after a couple of years they released an other song, the chorus of which was the chorus of their previous hit song in reverse. And it became a hit one more time! Funny, that the band never hid the fact, yet I've seen several threads on forums shouting they "discovered" the secret!
On topic no, I never played them backwards, simply because I missed the LP era. As a JW I don't think I heard anyone talking about hidden satanic messages, only about the dangers of clear messages when listening to songs in other language (huh? what influence on earth could have on me a song that sounds like a lullaby, but in gudjarati it sings "worship Satan"?) - I did hear the "backward message" rumors from other sources though, mostly hard rockers, who were proud of it
Correction, while playing a bit with digital audio editors, I did reverse some songs too, but not to look for any hidden message.