Are documentS created with Microsoft office for windows and Microsoft office for mac are compatible with each other

yes.

As with a lot of software, it depends on the version of Word, and what features the author used.

Technically, Office 2010 for Windows and 2011 for Mac are supposed to be feature compatible. As are Office 2007 for Windows, and 2008 for Mac.

However, if a person using Office 2010 / 2011 used a feature that only exists in that version and sends the file to someone using Office 2007 / 2008, they would very likely have trouble opening the file, or having it display as intended.