Talking about the covers which became more or even popular as original versions I'd mention:
Warm Leatherette - Grace Jones (The Normal, real name - D. Miller)
Memphis, Tennessee - Silicon Teens (one man fictitious band - D.Miller) - it isn't more famous than the original, but it gave a new life to it, this version was also used as a soundtrack in "Planes, Trains and Automobiles" (originally - by Chuck Berry)
I Will Always Love You - Whitney Houston, a soundtrack in "The Bodyguard" (Dolly Parton)
American Pie - Madonna (Don McLean)
Smooth Criminal - Alien Ant Farm (Michael Jackson - it wasn't as famous as the original but very successful indeed!)
Behind Blue Eyes - Limp Bizkit as a soundtrack in "Gothica", with lyrics changed (The Who)
It's My Life - No Doubt (Talk Talk)
A Little Respect - Wheatus riched the higher chart position then the original (#3 vs #4), Kim Wilde performed it on tour (Erasure)
Solsbury Hill - Erasure (Peter Gabriel) - it reached the higher chart position than the original (top10 vs top 20)
The Shoop Shoop Song (It's in His Kiss) - Cher gave it the second life, and it was a massive hit in 80's (Betty Everett)
Somethin' Stupid - Frank & Nancy Sinatra, Robbie Williams & Nicole Kidman (Carson Parks & Gaile Foote). Williams & Kidman version is hardly known in America, but it was a huge hit in Europe.
Some "heavy sampling":
Sugababes used a significant piece of Sting's "Shape" in their own "Shape"
Rihanna used a sample form Soft Cell's version of "Tainted Love" for her "SOS"
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