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1965's "See My Friends" was the first song that had a sort of mystical quality to it. It's also proto-psychedelia. And it was influential. According to the Wiki, Pete Townshend said at the time:

See My Friends' was the next time I pricked up my ears and thought, 'God, he's done it again. He's invented something new.' That was the first reasonable use of the drone—far, far better than anything the Beatles did and far, far earlier. It was a European sound rather than an Eastern sound but with a strong, legitimate Eastern influence which had its roots in European folk music. link

The drone sound that runs through the record was accidental -- much like the sound of the guitar in 1964's "You Really Got Me."

Ray Davies explains:

I played the song for the first time to my two sisters in Muswell Hill, using this beaten-up 12-string Framus guitar. It had a great quality, but when I played it in the studio, I got too close to the mike, and it started to feed back. And that provided the drone that ran through the record. I remember Shel Talmy saying "we'll never get all this sound on there, so I'll compress the shit out of it.' It ended up a mixture of my stupidity, Shel's opportunism and engineer Bob Auger's technical ability. I'm not sure it's a great song, but it's a great record.

In a widely quoted statement by Barry Fantoni:

I remember it vividly and still think it's a remarkable pop song. I was with the Beatles the evening that they actually sat around listening to it on a gramophone, saying 'You know this guitar thing sounds like a sitar. We must get one of those.'

Six months later, The Beatles released "Norwegian Wood."