Go to www.whatismyipaddress.com .
While there are other websites that do the same thing, this is the only one I know of with a URL that is easy to remember, and pronounce. This is what to do if you're troubleshooting a computer over the phone and need to know its IP address.
Websites like these will give you the IP address of the computer that actually connects to the server and fetches the page. This is not necessarily the computer that the web browser is running on. If you're using a proxy, it will be the ip address of the proxy. If you're on a network with cascaded proxies, it will be the one furthest down the chain. If you're using NAT, it will be the IP address of the NAT machine. If you're on something more complicated, such as transparent proxying, it could be anything.
Other services like this include:
URL 1 is special - it uses SSL, so the communication with the server is encrypted. This means that transparent proxies can't intercept it. It is very likely that the results of URL 1 are the IP address of the computer the browser is running on. If you suspect a transparent proxy, visit urls 1 and 2, and if they come up with different numbers, you're stuck behind one.
As an aside, computers don't have IP addresses, IP hosts do. There may be more than one host per network device, and more than one network device per computer. This is how your IP address can be 127.0.0.1, 192.168.0.1 and 126.96.36.199 all at the same time. If you're running linux, you have full control over the mapping of IP addresses to network devices. Most distributions ship such that 127.0.0.0-127.0.255.254 are all valid loopbacks. 127.0.0.1 being the loopback is only a standard on the Internet. On your own LAN/WAN you can set your IP addresses any odd way you like.