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For me, 1988 is a great year for music. My favorite all-time band, The Wonder Stuff, released their first album. So did The Posies, NWA, Tracy Chapman, Jane's Addiction and Melissa Etheridge, while Talking Heads bowed out with what is IMHO their best song.
So much good music I want to name them all, but perhaps it would be better for you to just check it out yourself.