Love-affairs of Zeus (to name a few):
   with mortal women:
  + Io (> cow)  =  Epaphus, fore-father of nations
  + Europa (bull)  =  Minos, king of Crete
  + Leda (swan)   =  two eggs; each hatched twins:
       Helen of Sparta (= Helen of Troy)       Clytemnestra
       Castor
       Pollux   Dioscuri (= Zeus' Boys)
  + Danae (golden shower) =  Perseus
  + Alcmene (husband) =  Heracles
  + Semele   =  Dionysus (ascension of Semele)
   with goddesses:
  + Metis, Titaness (swallowed) = Athena
  + Leto   =  twins:
       Apollo
       Artemis
  + Demeter   =  Persephone
  + Maia, nymph  =  Hermes

Hera retaliates by giving parthenogenetic birth to Hephaestus - the arch-craftsman of gods, lame. Married to Aphrodite & divorced.
Water gods: all know future. - Proteus; Ocean & Oceanids; Nereus & Nereids.
Lesser gods: Pan; nymphs; satyrs.
Gods periodically scheme and rebel against Zeus. He keeps them under control with the help of Hecatoncheirs and Cyclopes.
Actually, it is the Moirai (3 sisters: Clotho; Lachesis; Atropos) who really are in charge of the universe. They are weavers: Clotho/ Spinner weaves the thread of life; Lachesis/ Chance measures it; Atropos/ Inevitable One cuts it.  Even gods fear and obey them. They mind their own business, however, and report to Ananke/ Necessity.
Basic rules:
1. No god must undo anything wrought by other god.
2. Any god who has sworn by the waters of the river of death, Styx, must keep his word.
3. Gifts and favors of gods, as well as their love, usually bring disaster to mortals.