The Romans, for one, certainly were and did. During the regal period and early republic, they had the habit of praying or "calling out" to the gods that "lived" in and protected rival cities before battle in order to win them over, going as far as to promise sacrifice in exchange for victory. I believe this practice is called evocatio. I find it extremely interesting that they thought they could essentially "bribe" their enemies' gods that way.

The one particular example that comes to mind is from the story of the siege of Veii in Livy, where the Roman dictator promises the local goddess Juno a temple in exchange for victory:

"An enormous crowd went and filled the camp. After the Dictator had taken the auspices and issued orders for the soldiers to arm for battle, he uttered this prayer: [2] ‘Pythian Apollo, guided and inspired by thy will I go forth to destroy the city of Veii, and a tenth part of its spoils I devote to thee. [3] Thee too, Queen Juno, who now dwellest in Veii, I beseech, that thou wouldst follow us, after our victory, to the City which is ours and which will soon be thine, where a temple worthy of thy majesty will receive thee.’ [4] After this prayer, finding himself superior in numbers, he attacked the city on all sides," - Livy 5.21

Source: http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.02.0026%3Abook%3D5%3Achapter%3D21

I'm not entirely sure how ancient you were referring too or if the bible can really be counted as a historical source but it was the only knowledge I have regarding this issue.

The bible references many different gods worshiped by others in the area. I will give a few verses as examples

1 Samuel 7:4 says

"Then the children of Israel did put away Baalim and Ashtaroth, and they served the lord only."

Where Baalim and Ashtaroth were the god and goddess of the Canaanite nations.

1 Samuel 5:1-5

"After the Philistines had captured the ark of God, they took it from Ebenezer to Ashdod. 2 Then they carried the ark into Dagon’s temple and set it beside Dagon. 3 When the people of Ashdod rose early the next day, there was Dagon, fallen on his face on the ground before the ark of the Lord! They took Dagon and put him back in his place. 4 But the following morning when they rose, there was Dagon, fallen on his face on the ground before the ark of the Lord! His head and hands had been broken off and were lying on the threshold; only his body remained. 5 That is why to this day neither the priests of Dagon nor any others who enter Dagon’s temple at Ashdod step on the threshold."

This mentions the Philistine god Dagon.

Numbers 21:29

Woe to you, Moab! you are destroyed, people of Chemosh! He has given up his sons as fugitives and his daughters as captives to Sihnon king of the Amorites

This verse mentions Chemosh as the god of the people of Moab.

Acts 19:27-28

27 Everyone will start saying terrible things about our business. They will stop respecting the temple of the goddess Artemis, who is worshiped in Asia and all over the world. Our great goddess will be forgotten! 28 When the workers heard this, they got angry and started shouting, “Great is Artemis, the goddess of the Ephesians!”

This mentions Artemis, the Greek goddess as the goddess of the Ephesian peoples.

I would say that this gives evidence that the early Jewish people were fairly aware of the religions of their neighbors and in terms of passage about Dagon at least they saw them as merely false idols.

Yes, well some were. The primary examples are the Hebrews and cultures in the Bible and the Romans and Greeks.

For the Romans and Greeks there was a practice called syncretism were they had no issue with adopting each other's gods. They believed a kind of fluid view where each culture had a sort of facet and they were just different names. Now there is a bit of evolution and difference that comes with cultures changing.

This can be seen as opposed to, primarily, the Hebrews who were extremely monotheistic (with some caveats, sort of). At least by the second temple area (around Jesus' time) there was a belief that to say the holy name (YHWH) was, to say the least, inappropriate. In fact this developed so much that the pronunciation was lost (it is one of the reasons you have both Jehovah and Yahweh as spellings, that and Hebrew texts didn't include the vowels)!

Now the Hebrews are an interesting group because depending on who you ask their syncretism was more prominent or less. Now this is before the second temple period above and more during them being in Canaanite and potentially Egypt and Canaanite again with Abraham (again depending on the historian).

This discussion has to do with the Semitic word El. It was used as a proper name in Canaanite deities, and like Zeus, was the grand ruler. Like Kronos El also lost power to Baal though El is often described as merciful and the creator. As I'm sure you can see the parallels.

So what does this have to do with your question? There are generally two views of Judaism and their god Yahweh, one argues it came out of the Canaanite beliefs and was a simple offshoot that adopted characteristics into their god Yahweh. The other camp argues, in some manner, that this is not the case and any similarities are either not conclusive or have better explanations (for example if Abraham picked up the word "el" as a word for "god", similar to Allah in arabic [which is also descended from el!] and not to the specific Canaanite deity El).

What is clear however is that both Israel and Canaanite culture, after they were separate, did know of each other. Whether this is a 'memory' from the past or something that actually occurred the Bible portrays many instances of the Canaanites and Israelites clashing in Judges and so on. In Exodus it also shows knowledge of Egyptian culture and at least a small familiarity with their religion.

If you want to know more I'll try to help and if there are any confusions please ask for clarification.

If you want to know more there are a number of resources.

William Denver: Did God have a wife?

Warren Carrol: The Founding of Christendom Volume 1

(Academic; tough read) Mark Smith: The Early History of God

James Kugel: How To Read the Bible (related to that view is Scott Hahn Politicizing the Bible)

(Academic and a HARD read; I couldn't get through it) Frank Moore Cross: Canaanite Poetry and Hebrew Epic

Yale New Testament Series with Dale Martin (some information on the Romans and Greeks as well as Second Temple History).

Yale Old Testament Series (mentions El issue in their Exodus series).

James Hoffmeier: Israel in Egypt

Kenneth Kitchen: On the Reliability of the Old Testament

An example of syncresis in Roman Britain is the worship of Sulis Minerva at the ancient hot springs in the city of Bath (named for its springs, both now and in the past: the Romans called the city Aquae Sulis).

The Celts worshipped Sulis as the goddess of the springs, and the Romans rolled Sulis in with their own goddess of wisdom, Minerva, to have Sulis Minerva as the principal deity of the baths.

Wikipedia also says that "Sulis was not the only goddess exhibiting syncretism with Minerva." Other Celtic gods may have been similarly treated.

Herodotus wrote in the context of classical Greece at length of the parallels between Hellenic and Egyptian religion. As Livingston, 2002, notes, "One of the most frequently mentioned deities in Herodotus' account of Egypt is 'Theban Zeus.' Herodotus makes it abundantly clear that Zeus is known as Amun among the Egyptians."

In Histories, II (which is accessible online here), Herodotus writes of his inquiries to the priests at Memphis, Heliopolis and Thebes (who he assures us all corroborate the story),

The Egyptians, they went on to affirm, first brought into use the names of the twelve gods, which the Greeks adopted from them; and first erected altars, images, and temples to the gods; and also first engraved upon stone the figures of animals.

Herodotus emphasises his reverence of the religiosity of the Egyptians repeatedly throughout his works.

The Assyrians had Jahve (the Jewish god) in their Pantheon. Which the Jews (or citizens of Judea at the time) found very offensive.

In Sumerian and Akkadian times, gods lived in the temples as personified (deified?) stone statues, which they would actually feed and wash and so on. Each city had a patron-god, like Jahve for Judea, and in their histories of these times there are references to the patron god abandoning the city and going to another place. This must be assumed to mean that some other power sacked the city and took their god statue with them, as a way to gain strength and humiliate the defeated city.

This info is coming from a course on ancient Mesopotamian civilisation I did two years ago, and sadly I can't find the curriculum right now.

Amelie Khurt The Near East to 1200 BC is the only title I remember off the top of my head, which is an exhaustive, though somewhat dry, account of contemporary assyriology.