You might think, oh, well that is fairly obvious, Christianity pushed them out. It was the whole, "You shall not have any other gods before me." commandment. (Exodus 20:3) That, while most likely partially true, never really seemed like it answered the question for me. That command, while applicable to Christians, was given to the young nation of Israel 800ish years before Christ.
Another reason I wonder about this that the Greek and Roman gods are effectively the same. And it's not just that, Ashtoreth (Ashera), to the Phoenicians, and Ishtar, to the Babylonians and Assyrians, is Venus to the Greeks and Aphrodite to the Romans. (She was the goddess of fertility) The point here being that some of those gods had a very long run as gods worshiped by man in the (western/near eastern) ancient world. It's not like some of them were "just worshiped by the Romans". (Which would explain them "dying out" as Christianity moved in, but they have a longer running history than that.)
I believe it comes down to power. In Exodus 7 Aaron "throws down" his staff in front of Pharaoh and it becomes a snake. Pharaoh is unimpressed and calls in his "wise men" and they do their thing, and throw down their staffs and they turn into snakes. The evidence here is that worship of these ancient deities (no matter what name they were worshiped under) was powerful. There was something to be gained and I think "magic" and elemental influence (weather, land, etc) was effectively the draw in the worship of these old gods. (People wouldn't worship something if they didn't think there wouldn't be a result.)
Because of the above I've always found myself wondering, "What happened?" to those gods and the ancient power. Why doesn't that translate after Christ? I finally think I have my answer. (I seriously have been thinking about this, off and on, for the past 4 years)
Lets start in Luke 4:
"And the devil took him up and showed him all the kingdoms of the world in a moment of time, and said to him, "To you I will give all this authority and their glory, for it has been delivered to me, and I give it to whom I will. If you, then, will worship me, it will all be yours." And Jesus answered him, "It is written,
"'You shall worship the Lord your God,
and him only shall you serve.'"" -Luke 4:5-8 (ESV) emphasis added
Verse 4:6 is where I want to focus. In another translation: "And the devil said to Him, "I will give You all this domain and its glory; for it has been handed over to me, and I give it to whomever I wish."" (NASB) Yes the devil lies, but partial truths are also just as damaging sometimes. Here in Luke 4:6 Jesus doesn't argue with Satan.
Now lets flash forward to the end of Jesus' ministry on Earth. After He had died and risen again He spoke to the disciples (right before the "Great Commission") and said, "... "All authority has been given to Me in heaven and on earth." (Matthew 28:18 (NASB)) It looks to me what Jesus is saying here is that the Earth is no longer Satan's house. Things are going to be different now because of the ultimate sacrifice He made.
Now, don't get me wrong here, Satan still has power. I think though that the power he had back in the ancient world has been broken since the resurrection of Christ, which is why we no longer see wide spread worship of those ancient deities anymore. They lack the power they once had.
This is a working theory and rough at best. There is most likely a lot more supporting evidence in many different places, but I haven't dug it up. I'm sure someone could probably write a whole book on the subject. (If they haven't already) My little "disclaimer" is that this is an imperfect idea and there are bound to be general flaws in the thinking, it hasn't gone through any refinement. I feel like for me, however, that this is an answer to a question that I have been looking for.
~B.