There are many popular artists who had success in covering songs. Boybands such as Boyzone and Westlife had released tons of cover songs, and became big hits in many countries. Mariah Carey had iconic covers including "Without You". Even other A-list artists did so, and found success in their cover songs.
Other artists who covers or remakes an old song invites the original singers as featured artists. British boyband Blue did so a couple of times. They invited Elton John to cover his own song "Sorry Seems to Be the Hardest Word". Since it was a big hit, on their next album they covered "Signed, Sealed, Delivered", an original from Stevie Wonder. The latter was featured on Blue's version, along with Angie Stone.
Westlife also invited Diana Ross for their own version of "When You Tell Me That You Love Me" which became a UK number 2 hit. Diana Ross' original peaked at the same position in UK.
Phil Collins was also featured for the hip-hop version of "In the Air Tonight" by Lil Kim, but changed "Tonight" to "Tonite". That version is actually a part of the tribute album for Phil Collins, and the song actually sounded like a sample.
Talking about samples, there are songs which interpolates an old song, and featured the original singer. Sting is part of Craig David's song "Rise and Fall", which sampled Sting's "Shape of My Heart". Eminem also had Dido became a part of his song "Stan", which sampled "Thank You" by the latter. However, "Stan" became a hit first before "Thank You".