Well, the permanently open applications on my system are: claws-mail, Pale Moon (browser forked from Firefox), konqueror (TDE file manager), konsole (TDE terminal), and Aqualung (music player). Other good friends include kate, Inkscape, and OpenSCAD (despite its flakiness). And I get a lot of mileage out of DOSBox.
If the OP hadn't specified desktop software, I'd also name Portage.