Various
http://www.sysinternals.com/ In particular, look at PSTools, FIlemon and Regmon.  This are all free, and I use then all the time.
http://www.karenware.com/ I've heard nothing but good about this stuff, but I have yet to try any of them.  I am on her newsletter.
http://joeware.net/win/free/

Bandwidth tests
http://www.speakeasy.net/speedtest/ - can choose from various locations and get separate download and upload tests.  Pretty pictures too.
http://reviews.cnet.com/7004-7254_7-0.html CNET - I've used this a lot.

Help desk software:
http://www.somehelp.net/ "Free, simple IT help desk software"

Secure disk erasers
http://sourceforge.net/projects/eraser/
http://dban.sourceforge.net/ My coworkers have used DBAN "Darik's Boot and Nuke" with very good success, but no SCSI drives.

Compression Utilities
http://www.winzip.com/
http://sourceforge.net/projects/sevenzip/ 7-Zip I have not tried this yet, but looks promising.

Network traffic analysis
Windows NT, 2000 Server and 2003 Server all have an optional component Network Monitor that provides very basic ethernet capturing and analysis.
http://www.ethereal.com/ Pretty much the standard.
http://www.keir.net/software.html Superscan, written by Robin Keir program, but I think he sold the rights to Foundstone (see K9 in the home computer / email / spam section).
http://www.insecure.org/nmap/index.html "Nmap ("Network Mapper") is a free open source utility for network exploration or security auditing. It was designed to rapidly scan large networks, although it works fine against single hosts. Nmap uses raw IP packets in novel ways to determine what hosts are available on the network, what services (application name and version) those hosts are offering, what operating systems (and OS versions) they are running, what type of packet filters/firewalls are in use, and dozens of other characteristics. Nmap runs on most types of computers and both console and graphical versions are available. Nmap is free …"

Large Text Files
http://www.textpad.com/ A very powerful general purpose editor for plain text files I use it quite a bit.  It can handle large text files (1 GB or more) and do so much more than Notepad, WordPad or MS Word.  I use this a lot.

Help Desk Software
http://www.inet-sciences.com/ low cost, web-based work order or Help Desk software solution.

Remote Assistance
Remote Assistance is nice, but it's buried deep within the Help and Support in Windows XP, to speed up starting this, you can make a new shortcut (tested with XPSP2) with the below properties in the run line:
%windir%\explorer.exe "hcp://CN=Microsoft%20Corporation,L=Redmond,S=Washington,C=US/Remote%20Assistance/Escalation/Unsolicited/Unsolicitedrcui.htm"

Alternative Web Browsers
This are popular due to the fact that they are less susceptible to the vulnerabilities found in Microsoft Internet Explorer.  If you use one of these, please manually patch them as they won't update via Automatic Update or Microsoft Update services.
http://www.maxthon.com/ A GUI interface on the IE rendering engine.
http://www.mozilla.org/