127.0.0.1

Do you have your OS X firewall set to "stealth mode" (this would deny any ping attempts). You can turn this off in System Preferences - Security - Firewall - Advanced.

Matt

That address is known as the loop back address and is for the machine you are on.
If you are not getting a response, I have to ask are you sure you have a network card of any kind installed and working?

They can't do so if you're behind a router.

Do you absolutely need the ability to ping the address, or only to load it (which only requires that you have Web Sharing turned on, and the loopback address correctly entered in your /etc/hosts file, which it is by default). Also, make sure that you enter the full http://127.0.0.1/ and not just 127.0.0.1, which may attempt to query your ISP's DNS first (and fail).

Matt

Anybody on the outside of your network can only ping your router at its public address (although some routers themselves have a "stealth mode" denying this). If they're inside the network, then yes, they will be able to ping your local address.

Matt