Depending how you count, pronouns have either three or four cases (they, them, their, theirs; some people consider "their" and "theirs" the same case).
Normal nouns have only one. Or, in other words, there's no case distinction on nouns in English. The closest thing we have is the 's indicating possession, but this doesn't act quite like case-marking on pronouns:
- His and her orders
- *He and her orders
- The king and queen's orders
- ?The king's and queen's orders
- The Queen of England's orders
- *The Queen's of England orders
In other words, the 's is syntactically separable from the noun it modifies, while the case marking on pronouns is not. So I personally wouldn't call it a case, any more than I'd call for a case. (Other linguists might disagree.)
Note: Some syntacticians posit an additional "null" case for theoretical reasons; this is the case assigned to PRO in control clauses. But that's theoretical trickery more than anything else (so don't worry if that made no sense to you); I mention it here only for the sake of completeness.