While I am not a complete convert to free open source software, I appreciate its merits in many areas.
Over the past years I have been transitioning to free open source products for certain tasks due to various reasons. These vary from discontent with the performance or capabilities of paid for products, to a worry that I will no longer be able to handle files in the future (outside of university) unless I cough up a significant license fee.
My favourites that I would recommend, I will present briefly on this page:
1) Writing Documents - Typesetting
I typeset my documents in LaTeX - on the one hand, they look better, on the other, the output is a universally accepted pdf. In addition, LaTeX offers versatility not easily matched by other products via its extensive collection of packages.
For any form of scientific publication or even just other documents "for posterity" LaTeX is just the best choice. My Photography Guide is typeset in LaTeX, as is my BSc Thesis.
2) Plotting and Statistics
I have had some run ins with two large paid for pieces of software for statistics and plotting - both provided by my university. In neither case was I really happy with the result and found a better cross platform alternative - R.
R is a statistical language which offers extensive flexibility via packages and produces beautiful plots - it has thus become my package of choice for plotting any data.
Firefox - I know startup is slow, but the add-ons (don't overdo it!!) make it the best browser I know.
Chromium based browsers may be faster at starting up and marginally faster at rendering, however for a long time did not offer the same amount of add-ons - nowadays they do. Iron and OperaNext are my products of choice for chromium based browsers where I require them.