Elton John: "Goodbye, Yellow Brick Road" (1973). Much of the music tied to the series has been comtemporaneous, from the 1980's era where the series takes place. This is an exception, yet given the implications of the action and thoughts of the Jennings family, it makes sense, and was perfectly synced with each scene. John's songwriting partner Bernie Taupin, wrote the lyrics inspired by the 1939 film The Wizard of Oz.
The Jetzons: "She Has Won" (early 80s) It's down in the mix somewhat in the weed-smoking scene with Philip and his teenage admirers. The band, a pioneer New Wave outfit, lasted from 1981-1983, making the song a period piece.
R.E.M. "South Central Rain (I'm Sorry)" (1983), Playing when Philip says goodbye to one of these admirers, and also from the time frame of the series.