There have been lots of Windows and Mac OS replies to this thread, so here's a few Linux ones for a change:
i3wm. I've experimented with many tiling window managers over the years but none of them got me to switch. i3, however, is something else. It's extremely simple, intuitive and easy to configure, and it might give you a small productivity boost depending on your workflow. For me this is tiling WMs done right.
Sublime Text 2 and 3. It's rare to find multi-platform desktop software that works reliably on Linux, and ST does it exceedingly well.
Valgrind. It's a game changer for certain kinds of development.
Ruby. I rarely write scripts, because most of the time I can just run irb and do everything with an one-liner.
The apt package management tools, or just Linux package management in general. Whenever I'm forced to use Windows or Mac I realize how fortunate it is that in Linux we're able to apt-get pretty much anything.
SQuirrel (agnostic SQL client). It's not very well known but it's a solid client for anything that has a JDBC driver.
Transmission. I find it has the perfect balance of features and simplicity for a Bittorrent application. It does what it needs to do reliably and doesn't get in your way.
mplayer/mpv. This has been my media player of choice for what, 15 years? Back when my PC wasn't fast enough to play some video formats reliably, mplayer could do it if I killed everything else and used the vesa driver. No other software could do this.
Comix. This is probably the best software I've ever used for browsing images sequentially in a folder (not just comic books). The interface is so simple but has all the features one would need (automatically uncompressing files, fast thumbnail generation, fit-to-width zooming, etc).
youtube-dl. Give it an URL, it will download media from it, no questions asked. It's hard to find software that does the right thing as often as youtube-dl does.
curl. For the same reason as above.
ffmpeg. It can get quite advanced with the command line options but with just `ffmpeg -i format_in.<ext1> format_out.<ext2>` you can do any video conversion you can imagine.
And of course, the favorites that have been mentioned here and I couldn't live without (git, ssh, bash, vim, python, sqlite, postgres, nginx, redis).