(Debuted January 28, 1984, Peaked #4, 20 Weeks on the Chart)
It was pretty hard to miss The Eurythmics. In 1983, Their breakout song in the U.S. was "Sweet Dreams (Are Made of This)," which was all over the radio and MTV as it went to #1. The memorable synth line mixed with the bright orange hair of Annie Lennox to make the song and video a reminder of that moment in time.
Personally, I found the duo's second Top 10 hit to be more interesting. While an actual string section shows up here (though I didn't pay any attention to that at the time), the song eschews a traditional verse/chorus structure for two distinct parts -- beginning "Here comes the rain again" and "Walk with me..." -- that are separated by short instrumental sections. Where "Sweet Dreams" seemed to be pushed because it was new or innovative, "Here Comes the Rain Again" seemed to me to be a better song. Its success proved that the duo wasn't just another act that came out with one interesting song or video and then just disappeared. Fortunately, they stuck around for several more hits.
There's an interesting back story behind The Eurythmics. Where some groups form during a pairing of the leads, Dave Stewart and Annie Lennox were a couple first and became a musical act as their personal relationship broke up. As exes, they found the music had much more chemistry than it would have if they'd stayed together.