Natron: for cross-platform video compositing (Adobe After Effects alternative) at http://natron.inria.fr/
Synfig: for cross-platform 2D vector animation (Adobe Flash alternative) at http://www.synfig.org
Scribus: for desktop publishing (Adobe InDesign alternative) at http://www.scribus.net
FlashDevelop: for ActionScript development (Adobe Flash Builder alternative) at http://www.flashdevelop.org/
MyPaint: for intuitive full screen digital painting (Autodesk Sketchbook alternative) at http://mypaint.intilinux.com/
Radio Station Programming: LiquidSoap http://www.liquidsoap.fm/
Streaming: Icecast http://icecast.org/
Low bandwidth, low latency audio codec: Opus http://opus-codec.org/
Lossless audio codec: FLAC http://xiph.org/flac/
Video downloading: youtube-dl
VirtualDub - video manipulation software that does some things better than 99% of its competitors (including direct-stream processing, which for some reason most commercial editing suites don't). Not a replacement for Avid / FCX / Premiere / whatever by any means, but it does some stuff better than anything else.
Also, grep.
password manager: KeePassX[0] (or MacPass[1] on OS X)
KeePassX works cross-platform and there are ports for Android and iOS.
VLC for video playback?
I am fond of ardour for mixing audio recordings.
Lilypond is my favorite music notation software, but I have a predilection for text-based formats.
Of course TeX and its descendents remain world-class for serious document production, even if XSL-FO-based systems have made a big dent there.
OBS - Cross-platform broadcaster software (for recording and live streaming). Better than any of its competition in my opinion.
It's my own, but I'd like to think that Cachet (https://CachetHQ.io), although in beta is a good replacement for StatusPage.io
Zotero is an excellent EndNote alternative
OpenShot is an imovie like video editor, I like it because it's easy to use
Rhythmbox is a featureful itunes-like music player.
Audacity isn't protools, but it's great for mixing audio
FFTW -- Fast Discrete Fourier Transform. Reason: it routinely beats proprietary FFT routines on real & complex and single & multidimensional transforms, and with better accuracy.
QGIS: GIS software that isn't worse then the big closed source programs and is better at certain specific things.
iOS, take your pick: https://www.cocoacontrols.com
I'm happy with https://atom.io
LibreOffice: word processing
Blender : for 3D modelling.
- Greenshot: Screenshot capture
- Audacity: Audio editingScribus - Desktop Publishing/Layout
Blender - 3D design/animation
Subtitle Edit: for creating/editing subtitles
Emacs.
vim.
Free software (not open source) but really great stuff (I use them everyday):
Music player: http://mpesch3.de1.cc/1by1.html
Batch rename tool: http://www.bulkrenameutility.co.uk
Flashcards learning (open source): http://ankisrs.net/
That may sound silly but humble Notepad++ should be a part of your list of great opensource software. Although at first glance it does not require spending time on learning its functionalities it offers a lot of plugins that allow to replace proprietary software (i.e. I'm using XML-plugin and that allows me to work with XMLs without using specialised software like Altova).
Also TrueCrypt - I'm using it all the time (although there are changes in maintenance community the last stable version was proven to be clean - I still trust old good truecrypt)