Essential values of the dative

The dative is the case of the indirect object. It is the case of finality whether it indicates the goal of the action, or the person or thing interested in the action.

The dative expresses, among other things, ...

indirect object (or dative of attribution):
The dative indicates the object of something given, attributed and even taken away (more rare, but finds its echo in Romance languages like French).
Latinus filiam duci dedit (Latinus gave his daughter to the chief)
 
do uestem pauperi (I am giving this article of clothing to a poor man)

dative of interest:
The dative indicates in whose or even what interest something is done.
Romulus Romanis maxima gesserat (Romulus had brought to pass great things for the Romans)
 
There exists also a dative of possession, derived from the dative of interest, used with the verb sum:
fuit Romulo tota potentia (Romulus had total power [to Romulus was all the power])
 
mihi est liber (the book is mine)

After certain intransitive verbs that express attachment, proximity, interest or detriment, there is often a dative complement:
feminis pepercerunt (they spared the women)
 
studeo grammaticæ (I study grammar)
 
Note: studeo means “to have a taste for”.
aderant Sabinæ ludis (the Sabines attended the games)
 
Note: composites of sum behave this way

Some adjectives in this last sense also take their complement in the dative:
Romanis utilissima (things of the greatest utility to the Romans)
 
Romanæ amicus (a friend to [of] the Rome)
 
utilis ciuitati (things useful to the state)