In addition to the information and analysis contained in the above writeups, it should be noted that "Karma Police" bears a striking resemblance to The Beatles' "Sexy Sadie". The piano lines on Karma Police are very similar to Sadie Sadie (hearing the piano intro of Sexy Sadie the first time was absolutely uncanny), only much slowed down on Karma Police.
Additionally, a couple of lyrics in Karma Police seem to mirror those in Sexy Sadie:
"This is what you get when you mess with us." Karma Police
"Sexy Sadie, ooh, you'll get yours yet." Sexy Sadie
"Karma Police, I've given all I can, it's not enough...but we're still on the payroll
." Karma Police
"We gave her everything we owned just to sit at her table." Sexy Sadie
Interestingly, as I far as I can tell, nothing has been said officially by either Radiohead or the surviving members of the Beatles (or Michael Jackson's lawyers for that matter... haha) about the similarities between the two songs.
A case of inspiration by replication? Inspiration by unconscious rememberance? Or simple coincidence? We may never know. At any rate, this is one of those resemblances that don't really detract from the song - Karma Police stands on its own as a quite powerful piece of music and an important part of OK Computer, regardless of the similarities it carries on its shoulders.