You can go a very long way these days with free, open source, multi platform software.
What that means:
Free - No mandatory fees, but if you can donate, please do.
Open Source - The source code is available, and you can get involved in the development of the software.
Multi Platform - The software is available very often, for all three of: Windows, Linux and Mac
MEDIA PLAYBACK
VLC - A replacement for windows media player, will play almost any kind of video and audio file, as well as streamable formats, and playlists. It may not be able to replace i-tunes or Spotify, and is less useful now that streaming platforms come with their own players, but it's still a very useful piece of software to have both on your desktop/laptop, as well as your phone and tablet.
PHOTO EDITING
GIMP - The open source answer to photoshop. GNU Image Manipulation Program. Maybe not the easiest piece of photo-editing software to use as it's a full featured professional-level package, but it's well worth getting familiar with, as when you do you won't need any other software to edit photos, or any other image format. Also useful for converting between jpeg, png, jfif etc.
VECTOR ILLUSTRATION
Inkscape - The free alternative to Illustrator or Coreldraw. Not all image formats and image creation is pixel based. For vector image creation, that is shapes and text, specifically SVG files, this is what you need.
3D MODELLING
Blender - Not only is Blender the best open source 3D software package, it's really starting to hold its own as one of the best outright. The UI takes some getting used to if you're accustomed to a different 3D package, but it really is an amazing piece of software, and includes basic video editing and a decent Z-brush style sculpting tool.
EBOOK LIBRARY
Calibre - Calibre doesn't really have a direct paid-for equivalent, unless you count Adobe Editions or Kindle's desktop software. It is a great way of organising large E-Book collections and is largely compatible with PDF, EPUB, MOBI, TXT and AZW. Whilst it's mainly a library/organiser, it also comes with it's own reader software and several ebook conversion/reformatting utilities, as well as limited drm removal. (Plus extra functionality via plugins)
OFFICE
If you want an open source alternative to the MS Office suite of apps, you have two choices. Apache OpenOffice and LibreOffice. They both feature six apps: A Word clone, an Excel Clone, a Powerpoint clone, an Access (database) clone, a Drawing app and A Math formula editor. LibreOffice also features a charts editor. It's hard to say which is better, I've always used Apache until recently, I'm now using LibreOffice to see if it's any better. They were once the same piece of software, but for political reasons had to split into two. As they are both free it's well worth trying them both out.
VIDEO EDITING
Kdenlive - Is my open source video editor of choice right now. But I'm not completely settled on it yet, and there are a few other options in this space. I suspect one of them will become the main player, depending on which ones are maintained most regularly, or which are easiest to use. Olive, for example, has a version 2 in the works currently. There is also Openshot, which is said to be easier for beginners, and Shotcut has a more professional leaning user base. I'm going to play around with all four and maybe give them a dedicated write up at some point.
AUDIO EDITING & MUSIC CREATION
Audacity - Is a very good open source audio editing tool that everyone should have a their disposal. Unfortunately, there isn't very much out there for music creation, certainly not a full featured DAW that is open source and free. The closest I can find is LMMS - which is more of a midi sequencer, though it wants to be a full DAW, and may one day become one (remember how FL studio started out?)
I talk more about my audio setup in this post