Here's my list of things I use regularly that works just the same as my school's Windows/Mac applications. Most of these are art based applications, but I have some other things in the list too.
Final Cut Pro X, or any propreitary video editor, can be replaced with kdenlive. I havent done much video editting in kdenlive as I have to use FCPX at school, but kdenlive seems okay. Most other video editors are either Windows Movie Maker in quality (really basic) or I havent tried them out.
Photoshop can be replaced with Gimp. Honestly, I get more work done in gimp than in photoshop. It also looks better in my opinion, because you arent being lazy with a one-filter-does-all or the quick selection tool that photoshop has. Anyone who says that gimp can't do what photoshop does is 1) Being lazy and 2) Has never heard of plugins
Adobe After Effects can (somewhat) be replaced with Blender. Blender can do some pretty awesome simulations, post production and stuff like that to make effects that look really awesome. Integrating it with video is another story all together, but it can be done and I may show you guys an example of that later in a different thread.
Adobe Illistrator can be replaced with Inkscape or any vector graphics program really. Never really worked with vector graphics like Illistrator does, and I really dont care to learn it at this time.
Any music creating/editing software can be replaced with all of the following:
-freesound.org //For nearly any sound you can imagine
-http://www.bfxr.net //for making game sounds
-http://www.pulseboy.com //for making retro sounds (mostly DOS music, youtube it).
-Try banging things together, or actually recording the sound (within reason).
-Some general creativity
-And of course, Audacity for mixing/editting/putting everything together nicely.
Honestly, I think that recording your own sounds is the best approach. No harm in mixing any of the above sounds either.
Autodesk XSI, Maya, 3DS Max, and others can all be replaced with Blender. I used to use XSI, then I started using Blender and my artwork improved 100 times over, because Blender is awesome.
Unreal Development Kit, Source Engine SDK, or Unity can be generally replaced with something like Leadwerks Game Engine (non free). Leadwerks is okay, but I didnt really enjoy it that much. Never got too much into it either though. But for the $100 I say its worth it. One time fee of $100 for a FULLY featured engine, no limitations (unlike Unity's free version) I say it was a good buy. I will have to get into it in the next little bit here... I don't regret getting Leadwerks, thats for sure.
Microsoft Visual Studio can be replaced with Code::Blocks. While I've never run visual studio, I have Code::Blocks and I absolutely love it as an IDE for programming in C++.
Notepad++ can be replaced with something as simple as Gedit. Works great for me.
Although WINE is not an alternative program, it can be used to run just about any Windows application before ~2012 ish. Older stuff generally runs better. A lot of games run great in WINE. Just be prepared to do a LOT of tweaking to get anything working... Everything I've ran in WINE needed some sort of configuring before it worked. But at least it did work.
Hopefully I'm not restating anything to obvious. Just thought I'd chip in my two cents from an artists/programmers/gamers perspective.
Running on ancient hardware and a now super-charged linux only laptop. :D
Windows free since September 4th, 2014 @ 19:47 Mountain standard time.