Generally, you can use whatever naming practice you want to if you're working on your own. If you're cooperating with someone, it's obviously best to agree on some common standard, but that's between you and the others working on the project and nobody from the outside has any business or right to tell you what is the "right" or "wrong" way to name places.

In the specific case of the USA, I'd keep the "County" part to distinguish place names like these from each other:

* [Overlea, Baltimore, Maryland, USA][1] (neighbourhood in the independent city of Baltimore)
* [Overlea, Baltimore County, Maryland, USA][2] (unincorporated community and census-designated place in Baltimore County)

This also answers your second question: There are indeed places in the USA where counties do not exist. In particular, [Washington, D.C.][3] is not even part of any state and there are [41 independent cities][4] which don't belong to any county.


  [1]: http://en.wikipedia.org/wiki/Overlea,_Baltimore
  [2]: http://en.wikipedia.org/wiki/Overlea,_Maryland
  [3]: http://en.wikipedia.org/wiki/Washington,_D.C.
  [4]: http://en.wikipedia.org/wiki/Independent_city_%28United_States%29