In addition to OpenOffice Write (you download the whole OO suite, and Write is among the several applications included), and AbiWord, both of which I know are good, there is also:
http://www.writely.com/
I don't know how good it is, but it's been in the news because Google is about to, or has bought it, as a free web-based word proccessor. So instead of downloading, you'd just use it through Firefox or whatever your web browser is.
Just thought I'd toss Writely into the pool with the others for you.
I've used OO Write a lot. As a long time a native of MS Word, it was annoying to get the hang of OO Write. It does about the same as MS Word, but its menus are very different, with commands in unfamiliar locations that you have to re-learn. That makes you aware that you were (I was) on automatic pilot using MS Word.
Edit: It looks like Goole has it under the name
GOffice now, for $0.99 per month.