What was your love at first sight band? Talking Heads were on SNL and played "Take me to the river"(also first date with my wife, we saw "Stop making sense"
Have to agree with @BBJong below, Led Zeppelin is really good too. Love that song D'yer Mak'er from them, good song to make out to, some fond memories attached to that one.
When my wife and I met as English teachers in Korea, it was the late 80s, and Roxy Music was popular at that time. "Avalon" and "More Than This" became "our" music. More than ten years after her death, it's still painful for me to hear either one of those songs.
The Clash. Had already heard Should I Stay Or Should I Go and Rock The Casbah before, but when I first heard London Calling though...
That, and their other hit Train In Vain.