A Virtual Private Network ( VPN ) is good for this sort of thing.
It consists of a client (i.e. you) and a server which has been setup to act as a VPN. When you run the VPN software on your PC, it automatically routes all your Internet traffic to the VPN server. The server then acts as a gofer and fetches and sends all the requests you make whether its in Skype or your browser. The end result is all websites you visit only see the VPN servers ip address. This all happens nicely in the background untill you turn off the connection. You can use the vpn software on different internet connections as well. So if you do a lot of moving around it will connect fine.
There are two ways you can access such a service. One is to subscribe to a commercial vpn service. Once you subscribed they will tell you how to install the software on your omputer. Then all your Internet traffic will be routed through their servers. Prices range between around $10 - $30 per month depending on speed, gb per month you require etc. This is the easy way.
The other way is to rent a server yourself and configure it as a vpn server ( one great free software is called openvpn ). To tell you the truth I don't think this will work out economically for you unless you have some friends who you can share the server costs with.
Installing the stuff will usually require use of the command line and a basic knowledge of subnets, iptables and a little primer on public and private keys. If you don't know what they are or how they work I'd definatley go for the first option. If you still want to roll your own then you will find plenty of information on serverfault.com (sister site to this). I know, because i used it a lot to roll my own vpn to access the BBC whilst abroad. I was very green and it took an age.
Hope that helps
@Bob, I used to have residential Time Warner Cable. Whenever I changed the MAC of my router, the cable modem assigned me a new external IP address. See if changing the MAC address on your wireless card will do the same. Note that I had to disconnect, change MAC, reconnect; changing it on-the-fly didn't work. – hyperslug – 2010-01-08T09:28:35.413
@hyperslug: I've tried using macchanger which I installed on Ubuntu. I have successfully faked my MAC however I didn't get a new IP – Bob Dylan – 2010-01-08T09:39:44.703
Why do you want to change it? There aren't really many legitimate reasons to want to change it. – davr – 2010-01-11T01:23:30.407
@Bob, perhaps the cable modem or router assigns everyone the same external IP. Your IP may not be dynamic, but at least it's ambiguous. – hyperslug – 2010-01-12T02:35:54.157
2Bounty removed. Unless the ISP assigns an external IP to you there is no other way of getting or changing an external IP as already defined in the answer, adding a bounty will make no difference to the answers or the results. – BinaryMisfit – 2010-01-12T12:07:44.423