Now, here's a simple and clean widget - Show IP Widget.  Developed by XDA forum member mlbl, Show IP Widget (4 x 1 in size), displays your Android mobile device's Internal and External IP address in a widget.

The widget detects your internet connection on both WiFi and 3G to provide your IP address at a glance.  If your Android device is not connected, then the widget will display a 'Not Connected' message. Additionally, if you want to be able to copy your IP address to the clipboard, the widget also allows for that.

mlbl states that there are more features coming soon, since this is the dev's first attempt at creating a widget in order to learn more for development purposes.

Show IP address is available to download free from SlideMe - for more information and download link, visit the application thread.