Although the Greeks worshiped a plethora of Gods, there was also a shrine in Athens that wasn't specifically dedicated to anyone. It even appears in the bible in Acts 17:23, although Paul was immensely ignorant as to its meaning, thinking that the Greeks were "ignorant to what they worshiped," or perhaps Paul wasn't ignorant of what he was saying, but saw a prop for introducing the idea of the Christian god - maybe a bit of both. Paul's antics around the Greek world are very well known. He also visited Ephesus in 54 CE, where he was eventually ran out of town for organizing the large burning of ancient Greek and Jewish texts and trying to overthrow the present religious order, but he also ended up in Athens at one point, talking to the Athenians about one of their particular shrines. What we know for certain is that Paul's sermon was basically a trick to get the Athenians to think that they had already been worshiping Jesus or Yahweh without realizing it, for Paul was one of the best propagandists the new religion had in its arsenal. I am referring to the Shrine of the Unknown God.
The Shrine of the Unknown God was not, actually, dedicated to a God that was "as of yet unknown." It was actually established as a safety net, if you will, to make sure that no local Deity was neglected or forgotten, or who, at present, remained unnamed. The Greeks were not ignorant of the fact that many Gods were around, they just didn't know if they had named them all yet. So if a God didn't have a temple or a following, the Shrine was erected as a default sanctuary. You might even think of it like a temple or shrine to all the Gods, in the sense that it is not dedicated to specifically one, but all of them. It wasn't about ignorance of Divinity, but actually the knowledge and realization that Divinity is everywhere, and whether that Divinity has been named by us or not, it is still of importance and value. Even Paul's father god, aka the Jewish god, had an "unpronounceable name." In that sense, his god was also ultimately unknown. Generally, think about how many times you've heard a Christian say, "Don't question god," or "I don't know, that's just how god works." That's called an unknown, or an unknowing. When it comes to those things and those responses, Christians have constructed a Shrine of the Unknown probably more so than the ancient Athenians actually did.
With that being said, I still don't know if it was something practiced by every Greek City or town, and I haven't even heard of a modern Hellene having such a shrine today in their homes or temples. I personally wouldn't be opposed to having one myself, although I never have felt the need, and therefore if I did so, it would largely be to respect Tradition. However, I do, after all, live in a vast place which brings me to my final point about the Shrine of the Unknown, and that is humility. For an ancient Greek or a modern Greek worshiper to think that they know everything, especially about the Gods, would be hubris. Both ancient Greek and Christian religion advises against arrogance. What can be more humble than for someone to erect a Shrine that basically says, "I admit I don't know everything?"
In the Goodness of the Gods,