garrycl has suggested the best solution. I am currently running a website through my cable modem without a static IP:
Works like this:
You run a DynDNS client on your machine. When your IP changes, it automatically notifies DynDNS of the new IP, which in turn, automatically updates the IP linked to your domain name.
Simple concept...works great. Watch the traffic though. Your ISP will pick up on large volume hosting.
I use mine for exactly what you want to...to demo apps to clients. If they buy the app, I set up on a legit server.
Doing a live internet demo is a big selling point...it's easy to demo from a CD all day but that doesn't show them real world performance through their gateway and the internet.
And if you're like me...you're still broke. That means NO T1 line or expensive hosting equipment...or expensive static IP addresses.