Below is a list of software I use very often, and resources for the same. I also have included a list of programs that I install on every Windows install I use.

A good tool for creating documents, but it has a learning curve. LaTeX (pronounced la-TEK) enables you to write in plain text and generate good-looking PDFs for a wide variety of target audiences. The bundled templates are appropriate for many types of document/publications including presentations with Beamer, IEEE publication, and the standard report and thesis work which has lifted it to dominance in the realm of academic publishing. Add-ons are numerous and include the excellent TikZ package, Sweave, and many others.
A great text editor and my editor of choice. I am starting to maintain a page of Vim tips for the interested.
Software for creating and maintaining [mind maps], a highly effective tool for organizing thoughts or projects. FreeMind has a very intuitive set of default keybindings that allow you to “just use” the software from day 0.
A web-based HTML-to-PDF converter. It is distinct from the many other web-based tools because it treats HTML anchors correctly (i.e. generates a link within the PDF which goes to a different page rather than to the website). There is usually a better way to save web pages, but in a pinch I turn to this one.
I have contributed patches for this one. It’s a great tool for those of us with an autofeeding scanner because you can easily split PDFs.
Firefox/Tree style tab/Vimium/YouTubeEnhancer/UBlock/YouTubeAdBlock
Makes debugging/visualizing web pages and JavaScript very easy. I used it to get a lot of the direct-download links that are on this page. I also use the extensions linked above. In about:config, I set security.dialog_enable_delay = 0, app.normandy.enabled = false and browser.backspace_action = 2
Configure GTK themes–especially useful for those of us who don’t use KDE, GNOME or XFCE.
Window resizing in Microsoft Windows is annoying once you’re used to it on <insert name of other GUI here>. This helps.
Allows for easy configuration of Synergy using a GUI.
Fast PDF viewer for Windows. It’s good to have Acrobat Reader installed anyway because some PDFs only seem to print properly in it.
File manager that serializes the current directory listing to a file, and allows you to use $EDITOR to rename, delete, etc. files.
The best GUI file manager I have found; it is highly customizable.

New installation of Windows

Here is a list of programs that I normally install with Windows. This is mostly for my benefit when I am reinstalling for other people. Links below are to the canonical latest version when possible and will automatically start the download in some cases.

I also make some other modifications, such as

A shortcut is to install Chocolatey and just execute: choco install firefox git clink pandoc filezilla tortoisegit altdrag winmerge libreoffice ack.

Antivirus software

As of 2016, the following were useful for virus removal. I stopped using Windows machines around that time, and have not had to deal with virus removal. Better programs likely exist after 2019.