Like what? You mean like to check if one person really owns a address?
Sorry to be vague. I'd use it as substitute for a login mechanism.
Instead of a combination of username and password where the username is the internal identifier, I'd use solely a BTC address. For the login a random one-time-challenge string is shown to the user and he or she is asked to sign this string.
Example:
System: "Please sign the following message: login2113njsdfku3h24"
User answers with: G42O9cr+bwzfH71zfmFjIy/UmuQhVOxmqm5HgBglHMK/ceKCKBWSmLLd9sz8ZXpJxtAN0xwbyLyCwRjuUiQ7i/c=
The system verifies the signature and maps it to address: 17mDAmveV5wBwxajBsY7g1trbMW1DVWcgL
This address can then be used to recognize the user like the username before.
Oh well sorry I can't help you, since I don't know how to use the json rpc and had never heard of a signed message before... Is it like entering a random string in the public note section?