Other than acts mentioned, you had the alt-college bands led by R.E.M. making an impact. This really is its own genre of music. Also, the birth of electronic music and rap into the mainstream. Post-punk and new wave which have been mentioned (add Hoodoo Gurus, INXS, Blondie, Echo And The Bunnymen, Go-Go's, The Smiths, Midnight Oil)
You had 70's artists like Queen, Springsteen, Elton, Jackson Browne, Rod Stewart, Stevie Wonder, Genesis, Billy Joel, McCartney, Rolling Stones, ZZ Top, etc., still having great ouput (along with Bowie and others mentioned).
For melodic music that rocked it couldn't be beat (again sticking with artists not mentioned yet): Heart, Journey, Richard Marx, Foreigner, Leppard, John Cougar Mellencamp, Bon Jovi, Rick Springfield, Tears For Fears, Billy Idol, The Cars, Bangles, AC-DC.
Pure pop artists not mentioned with huge chart presence: Whitney Houston, George Michael, Olivia Newton-John, Laura Branigan, Kenny Rogers, Sheena Easton, Paula Abdul, Lionel Richie, Phil Collins,
My Best-Carey