Huh, I never knew about that myself. I was also going to ask what "signing" Bitcoin was. Do other clients have this feature, or just core?
Blockchain.info:
How can I sign a Bitcoin message?
Please log in to your My Wallet account, navigate to the 'Receive Money' tab, and click the Action option.

Armory:
Message signing with your Bitcoin addresses
Sign messages using the private keys of your bitcoin addresses, that can then be verified by someone else. For instance, you pay someone 200 BTC for merchandise to be shipped to you. You send the seller your postal address, but someone intercepts the message and replaces it with their own address! This is avoidable by using signed messages: the seller sees the money came from address X, so you send them a signature block, which tells them your postal address, and sign it with address X. If someone tries to change the address, the signature will become invalid!
Multibit:
https://multibit.org/en/help/v0.5/help_signAndVerifyMessage.htmlSign Message
You sign a message using a specific receiving address in a wallet. The recipient needs to know the address you signed your message with to verify it. To sign a message:
Select the wallet that contains your signing address in the 'Wallets Wallets' panel.
Choose the menu option 'Tools | Sign Message Sign Message'.
If your wallet is encrypted, enter the wallet password in the field labeled 'Wallet password'.
Enter the receiving address you are using to sign in the 'Address' field.
Enter the message you want to sign in the 'Message' field. Every character is part of the signed message, including spaces, tabs and line breaks.
Press the 'Sign Message Sign Message' button. The signature text will appear in the 'Signature' field and you will see a success message when this completes.
Send the message, the signature and the signing address to your recipient so that they can verify your message.
And I'm sure it goes on.