George Harrison of the Beatles was an accomplished guitar player with a distinctive soloing style. So you might think that with a song as personal and guitar-centric as "While My Guitar Gently Weeps," he would do his own playing. In fact, the song features guitar playing by Eric Clapton.
It was recorded on September 6, 1968, during the acrimonious White Album sessions. Harrison had been struggling off and on for over a month to get the song right. He first tried it with his own playing on a Gibson J-200 guitar along with an overdubbed harmonium. He later experimented by running the guitar solo backwards. Nothing seemed to work.
So finally Harrison asked his friend Clapton for a little help. When Harrison walked into Abbey Road Studios with Clapton, the other Beatles started taking the song seriously. In a 1987 interview with Guitar Player magazine, Harrison was asked whether it had bruised his ego to ask Clapton to play on the song.
No, my ego would rather have Eric play on it. I'll tell you, I worked on that song with John, Paul, and Ringo one day, and they were not interested in it at all. And I knew inside of me that it was a nice song. The next day I was with Eric, and I was going into the session, and I said, "We're going to do this song. Come on and play on it." He said, "Oh, no. I can't do that. Nobody ever plays on the Beatles records." I said, "Look, it's my song, and I want you to play on it." So Eric came in, and the other guys were as good as gold--because he was there. Also, it left me free to just play the rhythm and do the vocal. So Eric played that, and I thought it was really good. Then we listened to it back, and he said, "Ah, there's a problem, though; it's not Beatley enough"--so we put it through the ADT [automatic double-tracker], to wobble it a bit.
For the impression of a person weeping and wailing, Clapton used the fingers on his fretting hand to bend the strings deeply, in a highly expressive descending vibrato. He was playing a 1957 Gibson Les Paul, a guitar he had once owned but had given to Harrison, who nicknamed it "Lucy." You can hear Clapton's isolated playing above. And for a reminder of how it all came together, you can listen to the official version here.