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The Beach Boys
The Beach Boys were the one American band that not only survived as a hit-maker during the British Invasion, but actually managed to retain the popularity and compete with the top British pop bands (including the Beatles) for sales and chart rankings. Their career arc through the 1960s mirrors that of the Beatles. They hit the scene in the early 1960s as a band with catchy, simple pop songs. Their themes were the romanticization of California culture: beaches, sun, cars, surfing and girls. They created the West Coast pop culture that got exported throughout the United States and across Europe and even to Asia. Had this been their only stage, they would have still been one of the more successful hit-makers in music history and their surf pop would prove to be influential forever after, from other "sunshine pop" bands to punk like the Ramones to noise-pop bands like The Jesus & Mary Chain.
However, in the late 1960s, Brian Wilson began experimenting with production (influenced by the great Phil Spector's "wall of sound" production techniques) and opened a new era for the Beach Boys, that of the lush, sonically dense and layered pop that would prove to be influential not just in pushing their main competitors, the Beatles, to their own compositional heights, but to nearly every pop and rock band afterwards that created complex pop compositions. Brian Wilson and the Beach Boys are arguably the most influential band from the 1960s (the Velvet Underground has a great claim to that title, as well).
Everyone knows and remembers their masterpiece "Pet Sounds," which might be the greatest collection of gorgeous pop songs ever made and is always a contender for greatest album ever when lists are made. Less well-known are the albums before and after this magnum opus that spawned hugely recognizable gems that showed the evolution from surf pop band to sonic innovators (while never losing the knack for great hooks). Songs like "Surfer Girl" (who's name suggests a simple pop song but is actually lush and brilliant), "Help Me Rhonda," "California Girls," "Please Let Me Wonder" and "When I Grow Up (To Be A Man)" wouldn't have sounded out of place on Pet Sounds, but were tracks leading up to it, studding transitional albums of otherwise more straight-forward pop.
One of the great losses in music history is that the Pet Sounds follow-up SMiLE was never produced and released during the Beach Boys' hey-day, due to myriad factors, including Brian Wilson's declining emotional health, the rest of the bands' lack of vision in wanting to return to their tried-and-true surf pop hit-making and their label's aversion to risk, seeing SMiLE as a gamble in that it wasn't standard pop. Still, despite the album never coming together as Brian Wilson desired, much of it's material filtered out in albums coming after Pet Sounds, like Smiley Smile and Wild Honey. Tracks like "Surf's Up," (another deceptively titled song, for it isn't surf pop at all), "Heroes & Villains," "Wonderful," "I Was Made To Love Her," and, of course, the divine "Good Vibrations" (which is often a contender for greatest song of all-time, sometimes in competition with Pet Sounds track "God Only Knows") show the strength of the material that Brian Wilson was developing in the wake of Pet Sounds.
While the Beach Boys, amazingly, could be said not to have even reached their full potential due to resisting Brian Wilson's muse, they still produced an amazing amount of fantastic music through the 1960s and 1970s and their influence is in a class with very few other bands. Pet Sounds stands as their enduring statement of greatness, and as Paul McCartney (who participated in some of the SMiLE sessions by crunching vegetables in his mouth for a backing track) once said, that album may not have even been as good as SMiLE would have been. More concretely, McCartney said that what he heard in the SMiLE sessions sent him back to the studio, inspired to work on Sgt. Pepper's Lonely Heart's Club Band. So even the Beach Boys' unfinished symphony proved to have a huge impact on music.