The Replacements, along with Hüsker Dü's later work, for better or worse, shaped alternarock in the 90s. I'm talking from Nirvana to Gin Blossoms.
Let it Be is awesome, of course. So's Tim, with Pleased to Meet Me an admirable third. I haven't bothered with the rest.
EDIT: I originally mentioned Soul Asylum here, but I remembered they were around in the 80s, too, so it probably wasn't fair to include them.