When the era of the Summer of Love and Haight-Ashbury is invoked, often the first band that comes to mind, especially among those born later, is the Grateful Dead. Second is usually Jefferson Airplane.
This is one of the funny tricks of the passage of time; the further removed from history, the more it changes. Back in 1967 only the squares called anything "Haight-Ashbury". There were lots of scenes happening, thousands of scenes; some overlapped, some were isolated, some blossomed, some mutated, some broke down. They couldn't be pigeonholed by a street crossing name. Similarly, there wasn't really a "Summer Of Love" until Life and Look magazines called it as such and identified the Haight district of San Francisco as its epicenter.
But call the time and place what you will; there is one thing that is true. As respected as the good ole Grateful Dead was at the time, the band that represented the counterculture at large, the concept of the Summer of Love, Haight-Ashburydom, and better living through chemistry in the public imagination across the nation was Jefferson Airplane.
Jefferson Airplane was the first of the 60's San Francisco bands to hit big, and their photogenic, modern, countercultural, psychedelic, light-show-backed image appeared on magazine covers and the Ed Sullivan Show. As many have noted in the past, their career trajectory and musical sound perhaps best mirrored the evolution of the counterculture itself; from wide eyed lysergic innocence, through euphoric optimism, through hallucinatory psychedelicisms, through angry anti-establishmentarianism, through revolution, through drug absorbtion, through dissipation, through back-to-nature, to ultimate commercialism. Jefferson Airplane's timeline of 1966 to 1973 corresponds with the counterculture's perfectly; even Jefferson Starship reflects its day and age.
The thrills the Jefferson Airplane provided remain quite thrilling today; anthropology aside, they benefited in their classic period from the stunning three-part harmonies of leader Marty Balin, Paul Kantner, and Grace Slick. Jorma Kaukonen could effortlessly mix country blues picking with folk-rock conventional leads or some of the most cutting, expressive acid rock guitar ever laid to wax. Jack Casady rumbled underneath with a booming bass, bluesy, funky, or staid. Spencer Dryden brought in jazzy drums, a rarity in what began life as a folk-rock band. Balin, Kantner, and Slick were all good songwriters; Kaukonen became one over time, as well. Their music was capable of great beauty, and scary psychedelia. It was literate and acute. It was experimental, yet accessable. They were the only band to play all three of the biggest 60's festivals: Monterey, Woodstock, and Altamont (the Dead were present at Altamont, but didn't play). The group spun off two successful subgroups.