The old timers give the young'ns tips on the 60s.

Most of the music mentioned hasn't "fallen off the radar" as you wrote, but here are a few bands to also consider:

Amboy Dukes
Fever Tree
Steppenwolf (first 3 albums)
Guess Who (Canned Wheat)
MC5
Mothers of Invention
Blues Project
Paul Butterfield
John Mayall
Spirit
Velvet Underground
Beau Brummels
Fairport Convention

...don't forget 'iron butterfly'

I second Audiofeil's mention of The Blues Project, especially the album "Projections."

http://en.wikipedia.org/wiki/Blues_Project

Also, if you are interested in the folk genre, The New Christy Minstrels. Take a look at a list of some of their former members, in this writeup:

http://en.wikipedia.org/wiki/New_Christy_Minstrels

Also in the folk genre, Tim Hardin.

http://en.wikipedia.org/wiki/Tim_Hardin

Regards,
-- Al

After reading many of these posts, a simpler answer might be:

Look at the line-up on the 2 Woodstock album sets.

BTW, some different ways to go:

Late period doo-wop shows vocal music morphing into rock. You might consider The Showmen who worked with Allen Toussaint - a pioneer in this process.

Motown compilation. Berry Gordy's attempt to package black bands for the lucrative white audience.

Stax/Volt compilation - as above, but Southern fried and less "dressed up".

Listening to the radio and my brother spinning records during the late 60's and early 70's I grew to dislike a lot of these groups since I heard them over and over and over. One performer who I probably heard a few times but rediscovered a few years back was Tim Buckley. His music is more in the folk rock vein, but there's a sincerity to it without being too sappy.