Here are some useful tools for Network Administration. 

Tool: tcpdump
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By far the most usefull tool for a nework admin is tcpdump. This tool is presented in all good operating systems, FreeBSD, OpenBSD, NetBSD, Linux and Solaris, and other UNIXes. You will also find it here, with a lot of informations:
http://www.tcpdump.org/

Tool: netstat
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Very useful for a network admin, by default in FreeBSD, Linux and all UNIXes.

Tool: nmap
Site: http://insecure.org/nmap/index.html
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Very usefull tool to test your network/server security, to scan for open ports, gather informations about operating systems, mac addresses, computers on your network, and much more.

Tool: ntop
Site: http://www.ntop.org/overview.html
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ntop is a network traffic probe that shows the network usage, similar to what the popular top Unix command does. ntop is based on libpcap and it has been written in a portable way in order to virtually run on every Unix platform and on Win32 as well. Informations are accessible in a nice format from Web interface.

Tool: Nagios
Site: http://www.nagios.org/
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Nagios is a very usefull tool to monitor your servers. You can monitor a http server, an email server (SMTP, POP3, IMAP), a database server, and other services.

Tool: Cacti
Site: http://www.cacti.net/
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Nice tool to monitor your server, using SNMP. You can gather many informations with a lot of charts. Check screenshoots on their website.