I think that every Linux user has their own list of "favorite" apps which, for whatever reason, aren't included in the default distribution. Some of our choices may be driven by work responsibilities, while others make the list for usability...and it seems that most of us have at least one or two "just messing around" applications as well.
While I'm an 'occasional user' of several Linux distributions (Red Hat, SUSE, Linux Mint, and Fedora), I'm currently running Ubuntu 14.04 and 14.10; I make no guarantee that the applications I list are available for every distribution, or that the release offered in your distribution is the most recent; I've provided links to the home pages of the various projects, in case you want to run the latest-and-greatest stuff. Having said that, and in no particular order, here are a few of the apps I automatically install on any new Linux box:
Shutter: As a software support engineer and networking geek, I use screenshots on a near-daily basis - lots and lots of screenshots, particularly in chat sessions with my colleagues. Shutter is a comprehensive screenshot tool which includes the ability to save images in all major formats, export to sites like Imgur and Dropbox, annotate/edit images, and more.
Wireshark: The opening screen of Wireshark reads, "The World's Most Popular Network Protocol Analyzer"...and, well, they aren't talking trash. If you're doing anything interesting at the network layer, you NEED Wireshark. It not only does network captures, but also reads/writes the file formats of every major network analysis device out there. (If you're running Ubuntu 12.04, 14.04, 15.04 or 15.10, there's an official wireshark-dev PPA you can use to install the latest build (Wireshark 2.0-stable) instead of building from source code!)
Docky: OK, I'll admit it - I don't like the Unity Launcher provided by Ubuntu. Docky is a nice, clean application dock/launcher that includes a selection of useful docklets/helpers; it's almost trivial to customize Docky to your taste.
GIMP: (GNU Image Manipulation Program) This is my "just messing around" app; I like playing around with images, even though I'm not very good at it (just yet). GIMP has tons of features, including many into which I have not yet delved, but it certainly does everything I need to do as far as image maniuplation is concerned.
BOINC: I very much like the idea of digital philanthropy; if my box has idle time, why not donate it to a good cause? Well, the Berkeley Open Initiative for Network Computing (BOINC) client is a good way to go; there are dozens, if not hundreds, of scientific research projects to which you can donate your system's idle time via the BOINC client. My personal preference is World Community Grid, which has my systems currently working on genome sequencing and attacking the Ebola virus. Since I keep several of my systems running 24x7, there's lots of idle time while I'm sleeping - 'nuff said. (Personal request - if you decide to participate in WCG, use this link to register...and that widget on the right sidebar of this blog will pick up a "recruitment" badge. **grin**)
That isn't my complete list of "must have" apps, but it's a good start - feel free to add your favorites in the comments!