LibreOffice and its sibling OpenOffice...
Minor nit, LibreOffice is either a child or step-sib of OpenOffice since LibreOffice is a fork of the original OpenOffice.
Not a frequent word processor, more spreadsheets, so not completely germane, but my vote is OpenOffice/LibreOffice. And of the two, OpenOffice.
With the Apple stuff, they are slick UIs, especially on mobile devices, problem is, they like to do "Apple things" to the documents. For Numbers, as an example, when the spreadsheet comes back from Numbers as an Excel, cell borders are changed to hidden, every sheet is made into a "table" like sheet (got to spend time to reformat or copy/paste-special to a copy to remove the Apple-added formatting). Some formulas get totally changed (in one case, added extra math to existing formula). Now to be fair, Numbers handles Excel better than all other 3rd party Office-like apps I've tried re: formula compatibility and functions such as cross-sheet references.
OpenOffice/LibreOffice do pretty good re: going between Office and themselves. If nothing too "fancy" going on, no touch-up needed usually in Office.
OpenOffice over LibreOffice: yes, LibreOffice gets updated more often than OpenOffice, but that's not always a good thing. LibreOffice is too busy doing "cool" things with their updates, and that has added bugs. And in one particular case for me, created, fixed, and recreated the same bug (conditional cell formatting: initially put in a speed enhancement that broke the formatting, fixed the problem, a few releases later, conditional formatting broken again). OpenOffice is a little more stable, so if happy with UI and current version fits your needs...
ADD: to echo pingssgp's comment re: open. As per above paragraph, I've swapped between OpenOffice and LibreOffice over the last couple of years with no issues due to they "speak the same language", flexibility the locked formats from Apple and MS do not allow. And if OO/LO are not acceptable, NeoOffice is still out there, Lotus...
ADD2: TextEdit? If not doing anything fancy, might be a viable option.