-- Internet --
Even though it has recently been losing ground to Google Chrome the breadth and variety of extensions available for Firefox still vastly outnumbers what is available for Chrome. But even as that gap narrows the most important difference between them won't be changing. Firefox is created for a nonprofit organization to support a free and open web as much as possible and is not chained to a company's other product lines and marketing department's whims. For security's sake, the must-have plugin is NoScript. Open source freeware.
FTP, SFTP, and SCP Client:
SCP clients connect to a system using SSH and then allow file transfers through the encrypted connection. WinSCP allows both SCP and SFTP transfers, and it's open source freeware. It's also highly scriptable for automating transfers. Also supports plain old FTP.
The free PuTTY client can connect to system using Telnet or SSH, and it also has a UI for setting up SSH tunnels.
Ping and Traceroute utility:
Although quite old with its 1998 release date, TJPing 2.0 still works just fine on current-generation Windows systems. Use it to ping hosts, do name lookups, and perform traceroutes to see where packets are going, where along the way they're slowed down, if at all, and so on. They offer a Pro version, but the regular version is still freeware. I haven't yet found a newer replacement, but I must admit I haven't looked all that hard.
-- File Utilities --
Archiver with a graphical user interface:
The 7-Zip program beats out industry leader WinZip in all categories if you ask me. It touts its own 7z file format but works with several other formats and includes the ability to open some types of CAB and ISO files as well as good old gzipped files from *nix-like operating systems. Excellent Windows shell integration means right clicking anything gives you a variety of actions off of a 7-Zip context menu, and it doesn't skimp on the options for creating an archive that way. It's licensed under the LGPL.
Access to the highly compressed 7-Zip format on the command line makes this a valuable utility for automating compression and decompression tasks if you want to squeeze just that much more air out of your files. It also works just fine with the old ZIP file format.
Well known for playing a very wide variety of video and audio formats, the VLC Player can also stream media across your network and convert between some audio and video file formats. The newest 2.x version of the player sports improved Mac OS compatibility and a revamped UI. It's available for Windows, Mac OS, and Linux.
A powerful and flexible music ripper, organizer, and player. If you're not going to jump on the iTunes bandwagon then MediaMonkey can organize your music files for you rather well. Commercial software.
-- Graphics --
The Gimp is available for Linux and Windows. I tend to use it for dealing with screen shots and image conversions more than anything else.
Google's free Picasa program has grown remarkably over the past few years and the latest version is even available for MacOS. It has some great one-click features for balancing color in photos as well as an extremely easy-to-use and now partially automated red-eye reduction tool. If you use other Google services you'll like their even stronger integration with them.
-- Productivity --
Offering pretty good compatibility with Microsoft's suite, LibreOffice keeps things affordable for home users like myself with a $0 price tag and availability on Windows, Mac OS, and Linux. Open source and Freeware.
This text edtior is a far better text editor than the one bundled with Windows. It launches quickly, is small, portable, and has some nice features like syntax highlighting, line numbers, and more. Freeware.
-- Other Utilities --
Microsoft Security Essentials
It's Microsoft's operating system, why not let them clean up the mess caused by security holes and other vulnerabilities? Seriously, though, the security gurus have weighed in on this tool and found it works well. Security Now podcast guru Steve Gibson recommends every Windows user use it since it's free and works well according to experts he follows.
Maybe you need an external drive to be formatted Fat32 for your PlayStation 3. If so, Windows XP or Vista won't let you choose that filesystem for new volumes. Use the fat32format utility instead.
Got a bunch of Windows programs you keep open all the time, but don't want to have them clutter up your task bar? Tray-It! lets you specify any number of applications that will minimize to the system tray (by the clock). Freeware.
What software do you recommend?