Here is a quick summary of the more commonly-encountered cases of nouns and pronouns, for readers of Gaston Dorren’s book Lingo.

The ‘classical’ set, for example in Sanskrit:

Nominative – marks the subject of a finite verb – I hit him
Vocative – marks the person who you are addressing – Oh Sarah, what should we do?
Accusative – marks the direct object of a transitive verb – I hit him
Genitive – marks the possessor of another (pro)noun – my book
Dative – marks the indirect object of a verb – I gave him the book
Ablative – marks movement from, or a cause – I drove from Paris to London
Locative – marks a location – I live in London
Instrumental – marks the object used to perform the action – I cut the bread with a knife.

In English, most of these are accomplished using prepositions as shown, but many other languages inflect the (pro)noun instead.

Lumped groups include:

Oblique – marks the direct or indirect object of a verb, the object of a preposition, and some other uses (English)
Prepositional – marks the object of a preposition (Russian, Polish, Celtic languages including Irish and Scottish Gaelic, and others).

Others encountered less commonly may include:

Ergative – marks the subject of a transitive ergative verb (Georgian and other Caucasian languages, Basque, Kurdish, Hindi/Urdu, and others)
Partitive – marks partialness, without result, without specific identity (Finnish)
Comitative – marks something used, together or associated with (Finnish, Hungarian)
Causal – marks the purpose (Hungarian) Final – marks the purpose (Hungarian)
Translative – marks a change in state becoming, into (Finnish, Hungarian)
Elative – marks the limit in space or time of origination or initiation, out of, a locative (Finnish, Hungarian)
Delative – marks off, about, concerning (Hungarian)
Sublative – marks onto (Hungarian)
Allative – marks onto, similarly to, compared to, a locative (Finnish, Hungarian)
Illative – marks into, a locative (Finnish, Hungarian)
Essive – marks in the capacity of, by way of, as (Finnish, Hungarian)
Inessive – marks in, a locative (Finnish, Hungarian, Basque)
Superessive – marks on (Hungarian)
Adessive – marks at, on, a locative (Finnish, Hungarian)
Abessive – marks without (Finnish)
Exessive – marks from being (Finnish dialect)
Terminative – marks the limit in space or time, or destination up to (Finnish, Hungarian)
Instructive – marks with the aid of (Finnish).

Please do not hesitate to correct and augment these.