Case marking serves to discriminate between functions performed by Noun Phrases, i.e.
(a) grammatical relations: Subject, Object, Indirect Object, Possessor, etc;
and/or (b) semantic roles: Agent, Patient, Recipient, Location etc;

Intransitive verb:  S  V      (1) The girl was sleeping
                                              S(ubject)

Transitive:    A  P  V         (2)   The mother was feeding the girl
                                                     A(gent)                       P(atient)

(Note: the terms S, A and P are descriptive labels for the NP arguements of intransitive and transitive verbs. They do not entuilk that grammatical relations such as Subject can be identified in each language.)

Case marking and word order type

SVO languages: A precedes verb, P follows verb

                 S
             /       \
           NP     VP
           (A)    /     \
                  V     NP
                    |     (P)
         phom kin khaw  (Thai)
             I    eat   rice

Chinese, Thai: SVO languages without case marking
Russian, Finnish: SVO languages with case marking

SOV languages: both A and P precede verb

                S
            /         \
        NP          VP
        (A)        /        \
                  NP        V
                  (P)         |
kodomo-ga hon-o yon-da       (Japanese)
child-Nom book-Acc read-Past

Japanese, Hindi, Manchu: SOV languages with case marking

Greenberg (1966), universal no. 41: If in a language the verb follows both the nominal subject and nominal object as the dominant order, the language almost always has a case system.

2.1 Nominative-accusative ('accusative') system, e.g. Latin
 

Accusative case for object of transitive verb ('P')	same form (nominative) for S and A
(3) Puer puellam videt        boy girl-Acc sees     'The boy sees the girl'	(4) Puella  dormit        girl.Nom sleeps      'The girl sleeps'   (5)  Puella puerum amat       girl.Nom boy-Acc loves       'The girl loves the boy'

2.2 Ergative-absolutive ('ergative') system, e.g. Basque
 

Ergative case for subject of transitive verb ('A')	same form (absolutive) for S and P
(5) Ni-k  neska   ikusten dut       I-Erg  girl(Abs) see Aux      'I see the girl'	(6) Ni   etorri   naiz        I.Abs come Aux      'I have come' (7) Ni ikusten nau nere anaia-k       me see Aux  my brother-Erg     'My brother sees me.'

Greenberg (1966), universal no. 38: "Where there is a case system, the only case which ever has only zero allomorphs is one which includes among its meanings that of the subject of the intransitive verb". (i.e. only the S is morphologically unmarked)

2.3 Other systems

• neutral: no case marking (Chinese, Thai)
• tripartite: distinct forms for S, A and and P (rare: Wangkumara, Kalaw Lagaw Ya)
• stative-active (split intransitive, split-S): Case marking of S depends on verb type/semantic role of S

3. Distribution of case systems (based on Nichols 1992)
 

Type	Syncretism	Number of languages	Areal distribution
Accusative	S=A	93	ubiquitous
Ergative	S=P	28	Caucasus, S.Asia, Oceania, America, Australia
Stative-Active	S=A/P	21	America
Neutral	S=A=P	7	SE Asia
Hierarchical		5	America
Tripartite	S vs. A vs. P	1	Australia

4. Animacy and the Nominal Hierarchy in case marking

The animacy hierarchy: human > animate > inanimate
The Nominal Hierarchy: pronouns > human nouns > animate nouns
Person hierarchy: 1st person pronoun > 2nd person pronoun > 3rd person pronoun
                             (I/me: human)        (you: normally human)   (human or inanimate)
Definiteness hierarchy: definite > specific indefinite > non-specific indefinite

These semantic hierarchies determine:

(a) which NPs are likely to be case-marked at all

  English: she (Nom) vs her (Acc)  > it (Nom/Acc)
           who (Nom) vs. whom (Acc) > what/which (Nom/Acc)
  Latin: puer 'boy' (Nom: ' vs. puer-um (Acc) > bellum 'war (Nom/Acc)

  Spanish: "personal a" preceding animate objects

   Conozco a Juan
   know-1sg to John
  'I know John'

(b) which items are likely to be case-marked on a nominative-accusative and which on an ergative-absolutive basis

 Split ergative systems: NPs are 'split', with some marked ergative-absolutive and others nominative-accusative (Dixon 1994), as in Dyirbal (N.Queensland, Australia)
 

Pronouns: nominative-accusative	Lexical noun phrases: ergative-absolutive
ngadya nginuna balgan  I.Nom you.Acc hit 'I hit you'	balan  dyugumbil  bang-gul yarang-gu balgan CL2.Abs woman.Abs CL1.Erg man-Erg hit 'The man hit the woman'

References
Blake, Barry. 1994. Case. Cambridge University Press.
Dixon, R.M.W. Ergativity. Cambridge University Press.
Nichols, Johanna. 1992. Language Diversity in Time and Space. Chicago University Press.