I believe that the Beach Boys are the best American band of all time. For what it's worth, Rolling Stone Magazine agrees. They list them as #12 on greatest artists of all time, but they're the top American band listed (Link). Bob Dylan and Elvis are listed higher, but Dylan and Elvis were not bands.
The Beach Boys 11th album, "Pet Sounds," to me, is one of the greatest albums of all time. Rolling Stone lists it as the 2nd best album of all time. This album changed the course of music because it is the biggest influence on the Beatles Sgt. Peppers album. Paul McCartney says that "God Only Knows", from this album, is the best song ever written. There would be no Sgt. Peppers album, as we know it today, without Pet Sounds.
In addition to Pet Sounds, the Beatles had many other great hits and great albums. Their song "Good Vibrations" is listed by Rolling Stone as the 6th greatest song of all time (Link). Their song "Kokomo" peaked at #1 on Billboard in 1988. This meant that it was their first #1 hit in the United States since "Good Vibrations" in 1966, making it the longest time span between two number one hits in America for a band (22 years).
Having stayed together for over 50 years, the Beach Boys' longevity is incredible. Their 29th studio album of all new music came out in 2012 was reviewed well. It also sold well, reaching #3 on Billboard top 200. Guardian magazine said it's "the best thing Brian Wilson has put his name to in the last 30 years."