The Rutles are/were a very respectful (and accurate!) parody by Eric Idle (Dirk McQuickly) with brilliant songs penned by Neil Innes. Innes (Ron Nasty) was a sometime member of the Monthy Python team who later teamed up with Idle on his comedy series called Rutland Weekend Television, of which The Rutles were a spin-off.
The Rutles have a GREAT deal of respect among Beatle fans, and there was of course a seal of approval from an actual Beatle - George Harrison made a cameo appearance as the TV interviewer outside Rutle Corps!
There is a sequel coming out sometime in March 2005 apparently!