The Beatles. Everybody likes at least one of their songs because they have such a wide range of them. Probably my favorite two of the Beatles' songs are While My Guitar Gently Weeps and Octopus's Garden. Awesome songs.
How does this topic not have more responses!? The Beatles are great. At one time, I would have unequivocally said they were my favorite band, but I've branched out too much now. Still, I definitely like them a lot; they single-handedly created/popularized a lot of the more successful rock subgenres, if nothing else. Some of my favorite songs (that haven't already been mentioned) are Let It Be, In My Life, Rain, A Day in the Life, Penny Lane, and Across the Universe. On the other hand, Revolution 9 (different from Revolution) is one of the worst things I've ever heard.
You obviously don't understand what rock 'n roll is. Rock 'n Roll is a style of popular music that relies on blues-based rhythms and accentuated backbeats. The Beatles entire catalog of music fits that description. Pop and Rock are not mutually exclusive. Almost all Rock is Pop, but not all pop is rock. For example, guys like Frank Sinatra and Toby Bennett are Pop, but not Rock and Roll. Not every rock band has to rock hard, like Cream and Led Zeppelin, not every rock band has to be metal and misogynistic, like AC/DC or Guns 'n Roses. The Eagles and Fleetwood Mac, much like the Beatles, are neither of those, but are still Rock 'n Roll.
Also, as to the question of what genre the Beatles qualify as, let me just say that no matter what genre you consider the Beatles to be, they were extremely creative and made "more than their fair share" of excellent music.
I must preface my statement by saying that I made a mistake. I consider "Rock 'n Roll" to be stuff like Elvis, and that kind of thing that was popular in the 50's and early 60's. Rock, on the other hand, is music like Zep, or GnR, although I don't think AC/DC or GnR were metal, that's a bit of a stretch. So by this definition, the Beatles could have been Rock 'n Roll however I still classify them as 60's pop music. Although you could argue that, by definition, Pop Music is what is popular at the current time and at that time Rock 'n Roll was the Pop music but eh. Whatever.
I still personally don't classify the Beatles as straight up Rock or Rock 'n Roll, although I do agree that they contributed greatly to music as a whole, as @John_Smith said.
Also on the topic of great bands of the 60s. The Jimi Hendrix Experience, of course. =P Jimi didn't headline Woodstock for nothing.
Ugh how did I not find this topic before.... I currently own all their main albums sans Yellow Submarine. (That is, Please Please Me, With the Beatles, A Hard Day's Night, Beatles for Sale, Help!, Rubber Soul, Revolver, Sgt. Pepper's Lonely Hearts Club Band, Magical Mystery Tour, The White Album, Abbey Road, and Let It Be) Plus the Red and Blue albums and 1. ...jeez. They made a LOT of music. I love all of them. I haven't found a song by them I dislike.