I can't say I've ever been much of a fan. When it comes to '60s music, I far prefer bands like the Rolling Stones and Jimi Hendrix. The Beatles just always seemed a little to "cute" for my tastes.
The difference to me between the Beatles and practically any other band is that each individual...John, Paul, George, and Ringo...are all larger than life. Each is virtually an icon. With the Rolling Stones, you have Mick Jagger and Keith Richards...but it's not like the others are nearly as popular...I mean, Bill Wyman left the band and no one cared.
And the nature of the Beatle's music only adds to their universal appeal. It's completely non-threatening and accessible...to just about anyone...and any member of your family...as ITL says.