*AN
                                       + Antu
                                        (Anu)
                                     God of Heaven
          .---------------.--------------'|'------------.-------------.
       *Enki             Gibil      (4)Ninhursag        Shara      *Enlil
        + Ninki         (Gerra)       +Shulae                       +Ninlil
      (Ea, Nudimmud)    Fire God    (Ninmah, Nintu,                (Elli)
       Water God                   Mammi, Belittili)               God of Air
      (Lord Earth)                (Earth Goddess)                    |
    .------''----.                  '---.     .-----------.----------'`--.
(3)Marduk      Nanshe                   Ninurta           |           Ishkur
 +Sarpanit   (Morality                  +Bau           Nanna          +Shala
               Goddess)               (Ningirsu,       +Ningal      (Adad, 
                                          Nimrod)    (Sin, Yerah)   Teshub)
                                        War God(ess)  Moon God     Storm God
                                                          |
                            .-----------------.-----------^-----------.
                     (2)Nergal              Inanna                 Utu
                       +Ereshkigal          +Dumuzi                + Aya
                     (Irrigal, Erra)     (Ishtar (+Tammuz),      (Shammash)
                    God & Goddess of           Ashtoeth[??])      Sun God
                     the Underworld        Goddess of love
  Name
  +mate
  (alternate,
        Names)
Sphere of Influence 

Notes accompanying the family tree:
* Enki, An, and Enlil are the leaders of the Anunaki, Enki 'seems' to be the TRUE leader, with An more of a 'figurehead'.
1. These two are sometimes recorded as direct offspring of An (Ishkur in the Epic of Anzu, Inanna in the Epic of Gilgamesh); however Ereshkigal is consistently recorded as Inanna's sister, similarly Utu as her brother - therefore if she were to shift up the generations, arguably they should do likewise. Note also that gods are often misleadingly described as the 'son or daughter of An' as a poetic metaphor, perhaps to indicate that they are part of the main pantheon. The determination of his main offspring as shown is based on more substantial statements.
2. Nergal and Ninurta are sometimes assimilated with each other; I suspect this is because, in Enlil and Ninlil, Nergal is reported as their second son whereas Ninurta is not mentioned. Furthermore, in Erra (Nergal) And Ishum, Nergal is again reported as Enlil's son. Occasionally Nergal is also assimilated with Gibil - this may be due to nothing more than the similarity in their Akkadian names of Erra and Gerra respectively.
3. Marduk is only recorded as Enki's son in the Epic of Creation; he only came to prominence in the late Assyro-Babylonian period, so the importance attached to him by some must be viewed with some scepticism. Note also that he is so well known by this, his Akkadian name, that I have made an exception and used this throughout; his original Sumerian name was Asalluhe.
4. The fact that Ninhursag appears to be Enlil's consort in that they are Ninurta's parents does not detract from the fact that in Enki and Ninhursag she is clearly Enki's consort. The continual editing of texts, the assimilation of one god with another at various times, and the polygamous and incestuous nature of most relationships, mean that we should not get too hung up on such details. Although, of course, such changes in pairings may have a deeper esoteric significance


References:
1. George Smith, The Chaldean Account of Genesis (London, 1876), Chapter 4.
2. Samuel Noah Kramer, The Sumerians (University of Chicago Press, 1963), Chapter 4, pp. 122-3.
3. Stephanie Dalley, Myths from Mesopotamia (Oxford University Press, 1989), Glossary, pp. 317-331.