Open Office I use this free open source word processor and spreadsheet. It also includes a presentation program, a drawing program and a database program. I regularly use the word processor, Writer, and spreadsheet, Calc, in place of Microsoft's equivalent products. No problems to speak of. Documents can be saved in a variety of formats to ensure compatibility with most popular office programs.
Inkscape Free, open source vector graphics editor. I was a long time Corel draw user over the years but needed to upgrade. I thought about Adobe Illustrator but couldn't justify the expense. I had tried other free vector graphics editors in the past but was never happy with any of them for various reasons. Inkscape has proven to be solid and reliable and suits my needs, for free.
Gimp The free, open source alternative to Adobe Photoshop. While I do use Aperture to sort and store my photos, I use Gimp when I feel the need to retouch or adjust them. Tons of features and extremely powerful allowing you to keep things as simple or as complex as you need them to be. Lots of active users and developers so new features are always being added and bugs are addressed. Plug in support allow its feature set to grow.
VLC Allows you to open various audio and video formats as well as DVDs and streams. Does a ton of other stuff that I don't utilize but I am glad to have it all.
Flip4Mac Allows you to play WMV files in QuickTime. Very convenient.
Miro A free video player plus more with a really nice user interface. Watch internet tv and video podcasts. Built in BitTorrrent so you can download and watch from the same application. Subscribe to RSS feeds and watch YouTube content in HD. Internet TV.