This is a list of applications I frequently use (with a concise description usually taken from Wikipedia). What they have in common is the fact that they are free and run on both Windows and Ubuntu. I am lazy, I want to be able to work on the same file in different places with the same application.
They are all under further development (no blind tracks) and regularly used by me!
Firefox, Chrome: no words needed
muCommander is a lighweight, cross-platform orthodox file manager that will run on any operating system supporting Java
FreeFileSync is an Open-Source folder comparison and synchronization tool. It is used for fast and easy configurable sync operations between two folders without restricted or overloaded user interfaces
Diffuse: graphical tool for merging and comparing text files
Audacity. It is vastly famous, it is a an audio editor quite simple but very powerful.
FFMPeg and its siblings. It is an audio project based on a library with a constellation of visual interfaces using it.
GIMP is an image retouching and graphic tool. It is mainly oriented at raster manipulation.
Inkscape: vector graphics editor. Simple and powerful.
KeePass Password Safe is a free software password management utility for Microsoft Windows, with unofficial ports for Linux (KeePassX)
TrueCrypt is a freeware software application used for on-the-fly encryption (OTFE). It can create a virtual encrypted disk within a file or encrypt a partition or (under various Microsoft Windows OSes) the entire storage device (pre-boot authentication).
FreeMind is a free mind mapping application written in Java.