I use OpenOffice. (Link as above). It's a full office
suite so, as well as a word processor, it comes with a spreadsheet program, one for databases, presentation software, etc. If you choose to use it, I recommend changing the default 'Save' option, so that it will then automatically save files in Microsoft Word format (meaning that you'll be able to email files to others, safe in the knowledge that they'll be able to open them). Instructions here:
http://helpdeskgeek.com/office-tips/set-openof%EF%AC%81ce-org-to-save-in-microsoft-of%EF%AC%81ce-format-by-default/
OpenOffice has been created and developed by volunteers, in a similar way to how the excellent Firefox web browser has been developed. LibreOffice, on the other hand, started life as full commercial software (Lotus 123). When the company behind it decided to cease producing it, they placed the source code into the public domain and, like OpenOffice, it's now developed by a volunteer community. Just like OpenOffice, it's a stunning software:
http://www.libreoffice.org/
The 'new kid on the block', as far as free office suites are concerned, is Kingsoft's WPS Office Free:
http://www.kingsoftstore.com/kingsoft-office-freeware.html
Like both OpenOffice and LibreOffice, it's had very good press reviews.
As stated, all of the above are full office suites. If you're sure that you only need a word processor Abiword (which has been around since Fred Flintstone used his pedal-powered computer) still has plenty of fans:
http://www.abiword.org/
Finally, if you think that you might need to prepare something a little more complex than basic letters, etc, consider using DTP software instead of a word processor. Serif's PagePlus Starter Edition is free and excellent. (I've designed my Christmas cards with it this year!):
http://www.serif.com/desktop-publishing-software/?mc=FSSPAGEPLUS