OpenOffice is by far the most popular alternative (both among AB members and worldwide). SA has given you the link.
Libre Office also has plenty of fans here on AB though (and, like OpenOffice, is widely praised in the technical press):
https://www.libreoffice.org/
WPS Office Free (which was formerly called Kingsoft Office Free) is less well-known but, again, widely praised in the technical press:
https://www.wps.com/office-free
All of those programs can open files using any of the formats from the main components of Microsoft Office. (e.g. .doc, .docx, .xls, etc). The only exception, to the best of my knowledge, is that they can't open .pub files (but Microsoft Publisher is really an add-on for Microsoft Office, rather than a core component of it anyway).
All of those programs can also save files in Microsoft formats. (You might find, for example, that only .doc is available, rather than .docx, but everything you save can be opened by people using Microsoft Office).
The only compatibility problems I've ever heard of, from people using those programs, have related to handling documents which were saved into Microsoft formats using incredibly complex macros (which only about one person in several million is ever likely to encounter).
[I use OpenOffice, BTW]