Tension Software (http://www.tensionsoftware.com) has released version 2.0 of MyIP, a Mac OS X utility that lets you view public IP addresses to which you’re connected.
It can work also in background and can optionally show the current IP in the menu bar.
The public IP is the IP address you use to connect to the global net and is the address the rest of the world “sees” you at.
MyIP 2.0 is now optimized for Mac OS X 10.9 Mavericks. It costs US$0.99 and is available at the Mac App Store.