How can I notify my PC every time Android changes its IP? I'd like to send an email or post to a server every time the IP address on the phone changes. This way, I can continue to VNC into the phone, even when the IP changes. Is there an App that would let me send out the IP address, or a bash script I could use?
Rather than a notifier and managing all of this yourself, had you thought about using a Dynamic DNS client? This would allow you to always use the same name to contact your phone over the internet (or even a local LAN) and the 3rd party would manage the problems with changing IP addresses for you.

There are a number of Dynamic DNS clients on the Market, I haven't tried any, but it's a pretty common solution for machines that change IP, so I can't see why there'd be a problem.