Having introduced many MS Office users to OpenOffice.org, I would firmly respond that the best free-software office suite that is “like MS Office” is OpenOffice.org (minimum version 3, preferably version 3.1 or later).
Just about every major function of an office suite is not only provided, it's provided in a manner easily discoverable by people experienced with MS Office; the terminology and interface style lead such users to find things where they are already looking for them.
Plus it comes with OpenOffice.org Base, whereas (AIUI) MS Office typically doesn't come with Access; and it comes with OpenOffice.org Draw, which (AFAIK) has no comparable MS Office equivalent, and is fast becoming a killer feature over MS Office for some of the people I've shown it to :-)
There simply isn't a comparable free-software office suite that meets your stated criteria other than OpenOffice.org.