It is widely believed, among scholars of the history of Judaism and the Jewish scriptures, that the earliest books of the Tanakh display a gradual shift from a position of henotheism, to a form of monolatry, and finally, to an exclusivist monotheism.
The differences between monolatry and henotheism are somewhat subtle and hard to nail down, but my understanding is as follows:
Acknowledging that multiple deities exist and can be worshipped with validity, but limiting one's own worship to a single deity. Although henotheists usually worship the same deity their entire lives, it is possible to switch allegiances, so to speak; however, this behavior is more commonly associated with kathenotheism.
Acknowledging that multiple deities exist, and worshipping one of them at a time, but switching between the different deities at will. Usually considered a subset of henotheism.
Monolatrism [Also known as Monolatry]:
Acknowledging that multiple deities exist, but worshipping only one of them, and maintaining that the other deities are not worthy of worship. Usually considered a subset of henotheism.
Belief in a single deity, who is the only legitimate object of worship.
Note: Polytheists can sometimes also be henotheists (acknowledging the entire pantheon, but worshipping only one of the deities within it), but it is more common for them to engage in some degree of kathenotheism (acknowledging the entire pantheon, and worshipping one deity at a time, but switching from one to the next at will).
Thus the Israelites lived among the Canaanites, the Hittites, the Amorites, the Perizzites, the Hivites, and the Jebusites; they took their daughters in marriage and gave their own daughters to their sons; and they served their gods (Judges 3:5—6)
What god is there in the heaven or on the earth who can do according to your works and according to your mighty deeds?’ (Deut. 3:24)
For you, O Yahweh, are most high over all the earth. You are highly exalted above all gods (Ps. 97:9)
Now therefore revere the LORD, and serve him in sincerity and in faithfulness; put away the gods that your ancestors served beyond the River and in Egypt, and serve the LORD. Now if you are unwilling to serve the LORD, choose this day whom you will serve, whether the gods your ancestors served in the region beyond the River or the gods of the Amorites in whose land you are living; but as for me and my household, we will serve the LORD (Joshua 24:14—15).
Then [Elohim] said, “Let us make mankind in our image, in our likeness” (Genesis 1:26)1
[Elohim] stands in the assembly of El; in the midst of the gods he renders judgment (Ps. 82:1).
For who in the skies can compare to G-d? Who is like [Jehovah] among the [sons of G-d], a G-d who is honored [in the great assembly of the holy ones], and more awesome than all who surround him? (Ps. 89:6–7)
For G-d is the great G-d, and the great King above all gods (Ps. 95:3).
All the gods bow down before G-d (Ps. 97:7).
I know G-d is great, and our Lord is superior to all gods. (Ps. 135:5)
And the LORD God said, "The man has now become like one of us, knowing good and evil. He must not be allowed to reach out his hand and take also from the tree of life and eat, and live forever." (Gen. 3:22)1
"Come, let us go down and confuse their language so they will not understand each other." (Gen. 11:7)1
Do not follow other gods, the gods of the peoples around you (Deut. 6:14)
But you must not turn away from all the commandments I am giving you today, to either the right or left, nor pursue other gods and worship them (Deut. 28:14–15)
"You shall have no other gods before me” (Ex. 20:3)2
1The use of the first person plural (i.e., "us", "we", "our") implies that G-d is speaking to other beings who are roughly equivalent to Himself, in kind if not degree.
2This commandment wouldn't be especially significant for our purposes if it didn't include the words "before me". Scholars have long noticed that this inclusion suggests that it is permissible to have other gods, so long as G-d is always held above the others and given precedence and priority over them at all times. If the passage said only "You shall have no other gods", it would be unquestionably monotheistic, but as it is now, it clearly doesn't exclude the possibility that other gods exist - or even that these other gods can be worshipped, provided that they are accorded lesser status than Elohim.
I am familiar with the Christian explanations of these passages: it is usually argued that when G-d uses the first person plural, He is speaking to either Jesus and the holy spirit, or to the angels and the assorted hosts of heaven. In the more difficult to explain cases, other explanations are necessary. When G-d is described as sitting at the head of a council of gods, Christians say that the issue is one of translation, and what we read as "a council of gods" is actually a council of angels. When G-d makes explicit reference to other gods, Christians say that these other gods don't actually exist. I'm not convinced by any of these arguments, and I would like to hear what Jews have to say about it.