Networking Tools

Traceroute http://www.koepfer.de/traceroute
Traceroute utilizes the IP protocol `time to live' field and attempts to elicit an ICMP TIME_EXCEEDED response from each gateway along the path to some host. It is very useful to track where exactly your network is having issues or what backbones/routers a network is using.

Whois http://www.geektools.com/whois.php
You can use it for both domain names and IP addresses in order to find information such as registrar, administrator address/email, expiration/registration date, nameservers, etc.

Netcraft http://www.netcraft.com
Providing research data and analysis on many aspects of the Internet such as what's a host running or what's a host uptime.

ShowMyIP http://www.showmyip.com/
Will quickly give you information about your IP address and your browser User-Agent.

Start using cgi-proxy http://anaaman.blogspot.com/2006/01/start-using-cgi-proxy.html
A guide about how to quickly surf through an anonymous proxy without having to change your browser settings.