This may be more accurately phrased as how to survive using legally free software...

Browser: Mozilla Firefox

Newsgroup Reader: Mozilla Seamonkey

Vector Graphics: Inkscape

Image Converter: Squiggle, ImageMagick

LaTeX Editor: TeX Shop

Music: iTunes

DVD Ripper: HandBrake

Video Player: VLC

Generally Useful: Xcode, Image Capture (shift+command+4)