Just a few more:
1960's: The Kinks. Yes, I know, they have some popularity, but they are definitely overlooked compared to the Beatles, Stones, and Who. They had a revival in the late 70's-early 80's that was as strong as their earlier music, and more recently, Ray Davies has released some strong solo material. Neither Ray Davies nor brother Dave seem well these days, though, so we aren't likely to see this band again. Another mention would be Richard Thompson, who started in the 60's with folk/rock group Fairport Convention. Great guitarist/songwriter who is still making great music today.
1970's: Tough one, but I would go with Be Bop Deluxe simply because Bill Nelson (not the Dem senator) is a phenomenal guitarist and songwriter who is prolific to this day as a solo performer.
1980's: XTC has already been mentioned a couple of times but is deserving of another mention - probably the best band from the 80's that few people have heard of. Joe Jackson had some hits but is still making good music these days. The Jam burned brightly in England in the early 80's, but leader Paul Weller has had an even better career solo that runs to this day. Prefab Sprout has a dumb name, but they produced some great music in the 80's and early 90's. Someone else mentioned the Rainmakers, and I agree - Bob Walkenhorst should be a national treasure, but no one knows who he is outside of KS. I could go on about the 80's as I think it has been shamefully overlooked because Leftist music critics hate the Reagan era and everything associated with it.
1990's: Despite the lousy grunge and hip hop/rap music from this era along with the emphasis on indie music, there were still some solid acts. Ben Folds Five and Ben Folds solo, Tragically Hip, Uncle Green, Webb Wilder, and a few alt-country bands are notable performers that have been largely overlooked, but most bands from this era couldn't sustain any success for more than an album or two because they just weren't very good songwriters. That problem persists to this day.
Post-2000: Already mentioned Mouse On The Keys, but some of the other "math rock" bands like them seem interesting (no idea why it is called math rock, though). The Avett Brothers are pretty good, but, as with the 90's, you really have to dig to find truly talented songwriters/musicians. They are out there, I guess, but it is a real slog to find them.
I'm sure I've left out a few names, but this is off the top of my head.