When we use of in English, we are using a preposition to essentially mark genitive case. When we use 's, we are using a case marker on the possessor noun to mark the case. There are a large number of languages that use a suffix to mark case, including genitive case, so in that sense English is not strange.
The thing that is interesting is that English does not, for all practical purposes, have an overt case system anymore, except in a few rare and not-particularly-productive situation, and yet 's is quite productive.
The Saxon genitive came about as a result of the case system of Old English. In Old English, every noun was marked with case, as is done today in languages like Russian. It so happened that the genitive case marker for the masculine and neuter genitive singular was -es (Old English also had three genders, like modern German).
As the case and gender systems faded out of English in general, this -es form was generalized to be used on all nouns, singular and plural.
So, the reason English has the Saxon genitive today is because it used to have a full case system, and did not happen to lose this one particular case marker, probably due to its utility in showing possession.