In no particular order:
The Cure - In Between Days
The Cure - Just Like Heaven
The Clash - Rock the Casbah
The Clash - Brand New Cadillac
John Mellencamp - Rain On The Scarecrow
Tom Petty - Won't Back Down
SRV - Texas Flood
SRV - Couldn't Stand the Weather
ZZ Top - Legs
Pretenders - Precious
Tracy Champman - Fast Car
Prince - When Doves Cry
Probably nothing on this list with the exception of When Doves Cry that made it "big", but heck, I can't remember. Pretty much what I (still) like about the decade.
I might add that there's probably a Rolling Stones song or two that belongs on that list but for them the decades kinda run into each other.
Besides Prince, I would say Rock the Casbah, Legs and Fast Car definitely made it big. That’s without checking official charts.