Several languages have genitive cases, including Latin, Greek, Russian, Finnish and Sanskrit. Compare nominative case, accusative case, dative case, ablative case, vocative case, ergative case.
It is a common misconception that English nouns have a genitive case, marked by the posessive " 's " ending. Linguists however have shown that the English possesive is not a case at all, but rather a clitic, an independent word which however is always written and pronounced as part of the preceeding word. This can be shown by the following example: "The King of Sparta's wife was called Helen". Now if the English " 's " was a genitive, then the wife would belong to Sparta; but the " 's " attaches not to the word "Sparta" but to the entire phrase "King of Sparta".
That is not to say that the English possessive did not have its origins as a genitive case; but it has developed into being a clitic instead. In Old English, the possessive form of ban (bone) is banes. This developed, later, into the modern English possessive mark of " 's " as in "bone's." The 18th century explanation that the apostrophe might replace a genetive pronoun, as in "the king's horse" being a shortened form of "the king, his horse," is erroneous. Rather, the apostrophe is replacing the "e" from the Old English morphology.