Chances are if the other person can't open your document the they have an older version of word and it's not compatible with the format you're saving as.
Try saving the document as an RTF type - pretty much anything can read that.
As for Open Office being compatible with word - in my experience it's not quite so "Simples".
I've always run into difficulties with embedded pictures with Open Office and really doesn't seem to handle them half as well as Word does.
But if you just use simple docs then yes Open Office is fine