The Distributed.net project — a precursor to SETI@Home that used volunteer computer-time to attack giant, sophisticated ciphers — has cracked RC564. I used to have half a dozen computers working on this.
On 14-Jul-2002, a relatively characterless PIII-450 in Tokyo returned the winning key to the distributed.net keyservers. The key 0x63DE7DC154F4D039 produces the plaintext output:
The unknown message is: some things are better left unread
Unfortunately, due to breakage in scripts (dbaker's fault, naturally) on the keymaster, this successful submission was not automatically detected. It sat undiscovered until 12-Aug-2002. The key was immediately submitted to RSA Labs and was verified as the winning key.
(Thanks, Dave!)