Modern English has three or four cases (depending on which grammarian you're talking to):
|Case||Also known as||Used for||Examples|
|Nominative||Subjective||Subjects||I am a teacher|
|Accusative||Objective||Objects that are not reflexive.||Stella loves him|
|Genitive||Possessive||Possession||That's my car
Isn't it George's?
No, it's mine!
|Reflexive||-||Objects that are the same as the subject; identical agent and patient||He hit himself|
Sometimes the reflexive case is folded into the accusative. English's dative case has been all but lost and folded into the accusative. A distinction is only made between the nominative and accusative in some pronouns. Nominative and accusative nouns are identical in form and can be described as belonging to the common case.
Other Germanic languages tend to have more cases, and historical linguistics shows that the case system in English has been significantly simplified. Traditional grammar analysis often places an emphasis on case because it was derived from Latin grammar, and Latin has a significant case system. In modern scientific grammar however, its role is much diminished.