Pretty much all universities maintain a list of free-as-in-gratis software that they recommend students use. Very little of this is free-as-in-freedom software. There is no technical reason why most computer users should ever have to use proprietary software. Some users simply aren't aware of the drawbacks and dangers of proprietary software, while others are compelled to use proprietary software by institutions (their employer, etc.). It is vitally important that educational institutions do not compel, or even encourage, the use of non-free software, for many reasons.

The following list was initially based on the list of software Southern Cross University recommends their students use. I've supplemented this with other software I've found useful, and removed some items that solve problems that virtually nobody has these days (such as running Adobe Flash applications). Let me know if you've any suggestions.

Essentials

Software most students will find useful.

Audio players

• Southern Cross University recommends iTunes, which fundamentally is spyware. However,
• SCU also recommends VLC media player, and I would as well! According to Wikipedia, it runs on "Windows, macOS, [GNU/]Linux, BSD, Solaris, Android, iOS, Chrome OS, Windows Phone, QNX, Haiku, Syllable, Tizen, OS/2"!
• I use Totem for playing single audio/video files, and Rhythmbox for organising my music collection. These are only available for GNU/Linux (and other Unix-like OS's).
• gPodder is a pretty nice podcast downloader/organiser for GNU/Linux, OS X, and Windows.
• Suggestions, please…

File archiving/compression

• Southern Cross University recommends 7-zip, which I've used and recommended in the past. Runs on Windows, OS X, and GNU/Linux (though I use tar and gzip from the command line, or the GNOME front end to these). I don't recommend using 7-zip's own format for any important data you want to preserve for posterity. GZIP (or TAR and GZIP for multiple-file archives) is the most cross-platform and future-proof option, IMHO.

Java

• Most of Java is free software, though some components are proprietary.
• I use IcedTea, part of the GNU Classpath fully free software Java reimplementation, to run Blackboard Collaborate, and it works fine (that is to say, any problems can safely be attributed to Blackboard Collaborate). Only available for GNU/Linux.
• Would like to hear from anybody better informed than I about fully free software Java options for other platforms…

Mobile

• Mobile hardware and software is a privacy/security nightmare. You can at least not make the situation any worse than when the device came out of the box. F-Droid is a huge collection of free software for Android devices. Install the F-Droid app, and from there you can browse/search the collection and install the apps you need, knowing that there is complete and corresponding source code available for each, so the developers can't hide anything nasty behind a wall of copyright.

Office Suite

• By virtue of its feature-completeness, LibreOffice is pretty much the only game in town. I rarely used this kind of software before attending uni, and that's where 99% of my frustration with it lies. I've not found anything I've been required to do in three years of uni that it cannot accommodate, though I suppose Microsoft Office power users would face considerable migration strain. Runs on GNU/Linux, OS X, Windows, and even has a document viewer for Android.

PDF readers

If I had a penny for every time I'd heard PDF referred to as "Adobe Acrobat format"…

• I use and recommend Evince, which is available for GNU/Linux and Windows.
• The Free Software Foundation Europe maintains a list of many more free software PDF readers.

PDF writers/converters

• Southern Cross University recommends CutePDF Writer, which has been found in the past to install adware/spyware. Don't touch it with a bargepole.
• Many free software applications, such as LibreOffice and Mozilla Firefox, are able to export to PDF format without requiring additional software.
• Suggestions, please…

Utilities

• KeePassX remembers your passwords so you don't have to. Stores them in an encrypted file. Vastly preferrable to SCU's recommended (indeed practically enforced) solution: synchronising your passwords across multiple remote services! KeePassX runs on GNU/Linux, OS X, and Windows.

Web

• Most websites send executable code (rather than just the document you asked for) to your browser. That can provide useful functionality, which is fine (with qualifications) if you trust the source, but many sites also send programs from third parties whom they trust (or just don't much care about), while you are unaware of this. At SCU, your activities on the university-mandated ed-tech shambles that is Blackboard are shared not only with Blackboard Inc., but also with another half a dozen companies that provide services to the university and/or Blackboard Inc. (user statistics, caching or load balancing, and so on). These services are provided at a free or heavily subsidised cost, on the business model of surveillance capitalism. It is morally outrageous to require that students submit to this, but hey, every university does it (except maybe the good ones). The Electronic Frontier Foundation's Privacy Badger web browser extension is a reasonably user-friendly way to control which of these programs get downloaded and executed on your computer, and consequently whether a third party is able to track your use of any particular web site.

Nice to have

More specialised or advanced software.

Audio/video editing

• Audacity is a multi-track audio editor for GNU/Linux, OS X, Windows. A friend and I had a podcast for a while, so I used this all the time for cleaning up audio, and mixing elaborate sound effects from samples. It's brilliant.

Graphics

• Dia is a diagram (flowcharts, etc.) creation program for GNU/Linux, OS X, Windows.
• The GNU Image Manipulation program (GIMP) is a raster (bitmapped — photos, and so on) graphics editor for (according to Wikipedia) "[GNU/]Linux, OS X, Microsoft Windows, BSD, Solaris, AmigaOS 4". I don't do a lot of image editing, but I've depended on it for about 20 years, and have never once found myself wishing I had Adobe Photoshop.
• Inkscape is a vector (line art, logos, diagrams, etc.) editor for GNU/Linux, OS X, Windows.
• Dia, the GIMP, and Inkscape all export to PDF, and the latter two do a pretty good job of importing from PDF.

Reference management

• Bibus is a reference manager for GNU/Linux and Windows. It imports metadata in all the usual formats (Bibtex, etc.), though I've found it pretty poor in automatically generating references you can copy and paste into a list without manually tweaking. I find it principally valuable as a simple searchable database of stuff I can vaguely recall reading, but can't remember where. It has some functionality for hooking into LibreOffice and Microsoft Word, but I've not tried that. It's also unusual in that it doesn't try to hook you into using some proprietary web service, as most other reference managers do, so it wins on privacy.
• Unpaywall is a web browser extension for Firefox and Chrome which locates legal, freely available verions of paywalled journal articles, should they exist. Helps you avoid either your institution's clunky proxy system or [*cough*] informal alternatives.

Scientific/statistical calculator

• Speedcrunch is an intuitive scientific calculator for GNU/Linux, OS X, Windows.
• Qalculate! (you can tell it's fun by the exclamation mark in the name) is a plotting calculator that also has a lot more functions (including statistical functions) than Speedcrunch, though to my mind it's rather clunky to use. Runs on GNU/Linux, and a third party has contributed an OS X port.
• For statistical functions lacking in LibreOffice, and more heavy-duty number-crunching, GNU PSPP is excellent. It's a free software replacement for SPSS for GNU/Linux, though apparently you can get it to compile and run on OS X, if you're the sort of person who doesn't find that too intimidating.

Help wanted

Products that I've never had a reason to find free equivalents for. Suggestions appreciated.

Adobe AIR

A web app development environment. Possible alternatives.

Qualtrics

A proprietary online survey platform. I was a web developer in a former life, so I would use (and indeed have used) my own custom-built Drupal site to conduct surveys. I realise this is not a practical option for most students. The best solution for most would probably be a third-party platform licenced under the GNU Affero General Public License.

Deprecated

If you still need any of these, I'm very very sorry.

Adobe Flash Player

There used to be a number of free software alternatives, but as Flash is a dead technology, replaced by superior native web technologies, these projects appear to have died as well. While waiting for the corpse to be formally pronounced dead, install the HTML5 Video Everywhere plugin for your web browser of choice, and you can disable (and preferably uninstall) and forget the blasted thing.

Adobe Shockwave Player

Another superceded technology.

Microsoft Silverlight

A development/runtime platform for .NET applications. Not strictly obsolete, since .NET developers do perform the useful service of giving PHP developers somebody to look down upon.

Microsoft Security Essentials

An oxymoron in more ways than one.

QuickTime

Ah, memories.