There are a plethora of ideas, practices, innovations, and customs which originated in the pagan world and have been found true, praiseworthy, and useful by the people of God.
Some examples:
Math: (for instance, the Arabic concept of 0)
Architecture: most notably Roman advances, but also why do you think Solomon chose to hire pagan craftsman to build the Temple? (2 Chronicles 2:3-18) Because they had developed skills the Jews did not possess- excellent and praiseworthy skills.
Science: the medieval Christians gave birth to the scientific movement by combining their Christian worldview and their re-discovery of ancient Greek proto-scientists
Philosophy: The early church benefitted greatly from the bridges already built in Greco-Roman society by Socrates, Plato and other philosophers who, without direct revelation, nonetheless pointed their people closer to the truth. But not only that, these traditions helped Christians use abstract reason and theology in a way that their original Jewish heritage wasn't prepared to do.
Government: Don't know about you, but I would consider the idea of democracy as generally good, excellent, and praiseworthy. It's original appearance was, of course, in ancient Greece. And this tradition, melded with Paul's insistence on the equality of status in the church, led the world to some genuine improvements in governance. *
The above examples don't seem particularly religious in nature, perhaps. But I'd argue ALL truth is God's truth and there is not nearly as fine a line between the "sacred" and the "secular" as we are led to believe. Interestingly, that myth of a hard and fast division between the two does come from pagan sources, whereas the Jewish tradition has been much better at seeing how physical and practical things overlap seamlessly with the "spiritual".
That said, if you want some examples that seem more overtly religious, here are a few:
Many religious traditions that have made their way from the pagan world and have been baptized successfully into Christian tradition, because they contained some kernel of truth: Christmas trees, solstice-related festivals, use of musical instruments and art in worship, rhetorical skills used in preaching and writing, etc...
Keep in mind that Paul was a blend of the best of both Jewish and Greco-Roman (pagan) upbringing, and he was never afraid to use things he had learned from both sides of his background. For instance, he often quotes pagan authors favorably. He employs rhetorical skills he learned from the Roman side of his upbringing.
Or, take John, for instance, your favorite. It's pretty clear when he's writing to his audience about the Logos that he knows the connections they are going to make to Plato's philosophy about "logos". He is tacitly approving of it, though he is improving on it. The author of Hebrews taps Plato as well when he speaks of forms and shadows.
As to the passage from Deuteronomy 12, I think it's important to note that the emphasis is on not borrowing false pagan notions about who God is and what our relationship to him entails. The cultures Joshua led the Israelites against were particularly depraved, so what sparks of truth still remained among them were pretty drowned out by perversion. Still, as in some of the examples above, not completely, because the Israelites still found occasion to borrow some good, practical ideas from them.
I would also argue that, just as the New Testament authors describe the period of the Old Testament as the childhood of God's people, it is not surprising that as God's people grow up (or are at least expected to grow up), the hard and fast restrictions against mingling with other cultures begin to drop off, so that by the time we get to the New Testament, Christianity is finally going forth throughout the world, interacting with it, reclaiming all of God's truth that lies scattering like hidden pearls and bringing that wealth into the church (note how many times Isaiah mentioned the people of God bringing the "wealth of the nations" back to Jerusalem)
Now, all that said, is there danger in syncretism? Absolutely. Do we need to be very careful and thoughtful when interacting with ideas and religious traditions. Do we always need to look at everything in light of Scripture? For sure.
* as a side note, don't have time to dig it all up, but I recall when teaching through Kings that it stood out to me that when King David ascended the throne, he assembled his royal court almost entirely of pagans, probably because they knew things about governance and administration that pastoral Israel had no clue about.
