My favourites:
Dolphin and Konqueror. The best file managers I have found on any OS. Konqueror is also a web browser and document viewer. Weird but wonderful. Dolphin is more conventional but very slick. Both have excellent remote file and server connection management.
Kate. Great text editor, again, especially for remote files.
Geany text editor/lightweight IDE. Just feels natural to work with. Quite a lot of plugins.
Zim: "desktop wiki" - i.e. note taking and todo lists.
Terminator: tabbed, multi-pane, terminal emulator. Easy to organise when you have sessions open with a few remote servers and a few local windows.
digiKam - photo management
Okular - document viewer
My daughter's favourites:
Shotwell - photo manager
Thunar - file manager
Cross platform ones that deserves a mention because they should be better known:
Focus Writer - distraction free writing
Lyx - for presentations (usually PDF output).
Calibre - ebook management
Komodo Edit
Git Cola
GnuCash - accounts
Quod Libet - music player/library manager
Battle for Wesnoth
We also use a lot of better known cross platform software, from Firefox to Blender, but that is mostly stuff everyone who wants to knows about.