Debbie Harry played a huge role in transitioning 'new wave' into the mainstream in the late 70s and early 1980s. Her band, Blondie, emerged out of the same scene in New York that produced the Talking Heads, Patti Smith, the Ramones, Devo and others. Unlike many of those bands though they managed to achieve some level of popularity with punk and new wave audiences while still getting played on mainstream radio and in discos.
The band (on Twitter here) is still highly influential and their music is still covered and sampled by a wide range of artists. Blondie was inducted into the Rock and Roll Hall of Fame in 2006.
The first clip is the earliest I could find for the band, it's just a short clip of Debbie and the Band performing "A Girl Should Know Better" at CBGB in 1975 after that there are several full concerts capturing the band at the their height, starting with a show at the Beat Club in 1978, at Asbury Park in 1979, a show at the Apollo in 1979 and a 1982 show in Toronto, shortly before their initial break up.
Finally, for those who are really, really interested there is a 1999 BBC documentary on the band titled Beneath the Bleach and their 1999 comeback tour.
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