The legendary performers were all honoured with a dinner in New York, and representatives from all of the acts performed, apart from Genesis - who were instead tribute by the band Phish.
ABBA member Anni-Frid Prinzessin - who attended the show with singer-songwriter Benny Andersson, her ex-husband, from the group - said: "I am truly very touched by what once started as partnerships a long time ago, and that this has brought us here tonight."
Benny later performed a rendition of the band's song 'The Winner Takes It All' on piano, accompanied by singer Faith Hill on vocals.
Genesis attended the event, aside from original vocalist Peter Gabriel.
Drummer Phil Collins joked: "For people to come out and own up that they like what we do was very interesting, because we don't get a lot of that. It's very nice to accept music generally, rather than just rock 'n' roll."
Jimmy Cliff was on the verge of tears as he collected his award from producer and singer Wyclef Jean.
Jimmy said: "Reggae is a music that was not conceived in the United States like most of the music forms that we know. So to be standing here with you today, with a style of music that I was part of creating, is a great honour."
Iggy Pop - leader of The Stooges - took a more direct approach, saying "This thing is . . . heavy," when picking up his award, before showing two middle fingers to the crowd.
The Stooges performed their tracks 'Search and Destroy' and 'I Wanna Be Your Dog' at the event; Jimmy Cliff played 'The Harder They Come', accompanied by Wyclef, while the Hollies performed alongside Maroon 5 singer Adam Levine and Graham Nash.
The five annual entrants to the Rock 'N' Roll hall of fame are chosen by a panel of 600 US music industry professionals. Acts are eligible to qualify 25 years after releasing their debut record.