Wow. That is gonna be difficult. specifically the "century" part, as I can assume most people are not familar with the music from about 100 years ago.
I gave it a shot. Here is my list of 10 performers I feel are/were important to the music scene. How objective was I? Out of the 10 artists, I only own cds by 4 of them. The other 6 I don't listen to, or like very much, but I acknowledge their importance to the "scene".
Beatles-Although they generated the same hysteria we saw with New Kids or N'Sych, they were not the typical "boy band". More than pretty faces, they had innovative music, meaningful lyrics, experiented with sounds and styles, and bought Rock & Roll to homes all across Amercia.
Elvis-The ultimate showman. He understood the roots of Rock & Roll came from R&B. His musical style and stage presence showed that rock music could be a stage spectacle.
Janis Joplin- Although she didn't release a huge amount of music, her merging of folk and blues, as well as her outrageous style of dress, and behavior (usually reserved only for men) earned her respect in the music field after her death.
Led Zepplin- One of the pioneering bands of "Hard Rock". Took rock, and gave it an "edge" that found a home with a huge amount of music fans.
Black Sabbath- One of the pioneering bands of "Heavy Metal". Took hard rock in a new direction, and turned it into a sonic sledgehammer.
Aretha Franklin- A legendary voice, who combined her raw energy, gospel and R&B and bought a mainstream audience to "black" music. Continues to record, perform, and influence artists of today.
The Ramones- One of the first punk rock bands. They took rock, gave it a harder edge, and angry energy, and maintained it's integrity, while giving it mainstream attention.
Donna Summer- The Queen of disco. Her voice and performances helped bring disco out of the clubs and onto radio and tv. One of the few disco acts that managed to continue to have her new music played on the radio in the 80's & 90's, after disco was called "dead". Her success with disco allowed for more experiemtation with the genre, which lead to the evolution of dance music, giving us "house", "hi-nrg", "freestyle", and others.
Michael Jackson- Current troubles aside, Michael Jackson used his voice, and energy to bring he and his brothers (Jackson 5) to international success. Has one of the most successful solo albums ever (Thriller) and managed to cross barriers, having his music played on "dance", "rock" and "R&B" stations. Was one of the first black performers to break into MTV.
Madonna-starting out as a "disco/dance" artist (her first songs "Everybody", "Physical Attraction" & "Burning Up" were huge club hits) Madonna recognized the power of TV and image. She went on to write/co-write & produce/co-produce her own material, and helped bring dance music back to prominence on radio. Helped open the doors for many more female performers to get their music heard.