I made a list of the eight greatest 1960's bands. They're not ordered according to my favorite groups per se, but I took into account several factors like impact, popularity and productivity. Of course, the unavoidable subjective factor is still there.
Note: I only considered the bands that essentially belong to the decade, as some highly important bands like Led Zeppelin and Pink Floyd started their career during the 60's but they are essentially related to the 70's.
1. The Beatles. No need to talk about the importance of the Fab Four, especially in a forum like this. I don't like when some fans talk about the Beatles as if they were the only innovative musical force of the 60's, but they were certainly the most important part of the musical revolution.
2. The Rolling Stones. They never were very innovative, and during 1966-67 they basically copied what the Beatles were doing. But they certainly distilled a lot of talent, and in terms of popularity they were second only to JPG&R. The Stones were also a very productive band, with lots of classics songs to be remembered.
3. The Who. They're actually my second favorite band, since I consider them as a more talented act than the Stones; but their popularity and productivity were considerably lower. Pete & friends were highly innovative and diverse, bringing the loudest sounds of their time.
4. The Byrds. Not the band you're looking for if you just want loud Rock 'N' Roll, but like them or not, their impact in rock music is unquestionable. If they didn't invent folk rock, at least they made it popular, and they were also pioneers of as opposed genres as psychedelia and country rock.
5. The Kinks. Not as remembered as British counterparts the Beatles, the Stones and the Who, but they did record some of the best music of the decade. They started recording several important singles and then they released an amazing string of classic albums from 1966 to 1971.
6. The Beach Boys. Certainly the major Beatles competition during the first years, and one of the main forces of the fundamental mid-60's. They never were the same when they lost the best Brian Wilson, but only some selected bands can get such a huge cult following.
7. The Doors. Hardly any other band constructed their big image on one outstanding figure the way the Doors did with Jim Morrison. The other members were capable but never instrumental virtuosos, and Jim himself was far from being the best singer. But all their albums with the whole band are very enjoyable and they managed to build an unique mystic.
8. Jefferson Airplane. They had what the Doors lacked: instrumental virtuosity and good singers; and their sound was as obscure and intriguing. But they never got such an strong figure to lead them to the top. Nevertheless, they're an essential 60's act and the major face of the San Francisco sound.