What are the Twelve Tribes of Israel? The Bible frequently refers to the twelve tribes of Israel. Which tribes constitute this list? Jacob had twelve sons, but Joseph's two sons each got a land inheritance and Levi got none. So do the twelve tribes refer to those who had territories (thus excluding Levi) or to the sons of Jacob (combining Manasseh and Ephraim)?

When the names of the tribes were written, for example Exodus 28:21, how would the list appear? Would Joseph be written in place of Manasseh and Ephraim or would Levi be omitted?
Jacob had twelve sons by four women. They are: 


From Leah: Reuben, Simeon, Levi, Judah, Issachar, and Zebulun
From Rachel: Joseph and Benjamin
From Bilhah (Rachel's maid): Dan and Naphtali
From Zilpah (Leah's maid): Gad and Asher


Joseph, of course, had two sons - Manasseh and Ephraim.

The tribe of Levi was not given an inheritance, as we see in Joshua 13:14:


  But to the tribe of Levi he gave no inheritance, since the offerings made by fire to the LORD, the God of Israel, are their inheritance, as he promised them.


We see the separation of the 'House of Joseph' into the tribes of Ephraim and Manasseh in Joshua 14:4 (and a repetition of the Levite's inheritance)


  for the sons of Joseph had become two tribes--Manasseh and Ephraim. The Levites received no share of the land but only towns to live in, with pasturelands for their flocks and herds.


We can read in the rest of Joshua 13 the particular land each tribe was given (note that Manasseh actually became two half-tribes. One half was beyond the Jordan, and eventually disappeared from Israel).

The basis for Ephraim and Manasseh being full tribes is given in Genesis 48:5-6, as Jacob adopts them as if they were his own sons (as Reuben and Simeon):


  And now your two sons, Ephraim and Manasseh, who were born to you in the land of Egypt before I came to you in Egypt, are mine; as Reuben and Simeon, they shall be mine. Your offspring whom you beget after them shall be yours; they will be called by the name of their brothers in their inheritance.


So the twelve tribes can be listed as:


Reuben
Simeon
Judah
Issachar
Zebulun
Ephraim
Manasseh
Benjamin
Dan
Naphtali
Gad
Asher


We see this listing clearly in Numbers 1, and a final note on the separation of the Levites (v47-49):


  The ancestral tribe of the Levites, however, was not counted along with the others. The Lord had said to Moses: “You must not count the tribe of Levi or include them in the census of the other Israelites."