I leave all of them on all the time except for zombies and apocalypse.
Tech & Civic shuffle is great! I really enjoy the 'adventure' of finding my way through these trees and not knowing what specific items I need to select to get to a desired future result. It makes every game different.
Monopolies and Corporations I'm really liking, and it does seem that the tourism effect is better than it initially was, although maybe still too strong. One of the most interesting things is deciding where to put industries, and ultimately corporations, to provide maximum benefit to the intended primary output of specific cities, like getting tobacco in my military unit production city.
Secret Societies is fun, although I need to 'get out more' [i.e. try some different approaches]. I usually use vampires [or the society of assassins, or whatever you want to call them] for the 'free' unit initially; but the biggest benefit is the castle which I plan specific improvements around to enhance my capital's production, food, etc.
Heroes is fun. Unlike some, I've seen many heroes taken by the AI and used by them. Various heroes work best with different situations - like I always like Hercules [but don't always get him before the AI does] for the instant districts in low-output cities, plus he's very strong as a warrior after that. Similarly, Maui can be phenomenal for adding luxuries to a desert tile in a city with Petra! Just have to make sure 1) you get him and 2) you don't get the tile until after the resource is placed. Similar for others, like converting a unit with one hero [or building a really cheap unit] and have Arthur convert them to questing knights.
Barbarians adds a new dimension to the barbarian game - keep them, for city state benefits down the line? Destroy them because they occupy a place you'd like to put a city and/or for the 10 XP to the unit doing the actual destruction? Have to be careful though, I bought a ship from a barb camp ... and it ended up landlocked in a lake next to my capital! And with no place to do a canal to get it to the ocean.
Dramatic Ages adds another series of strategic decisions required to try to stay in a golden age - or have troops ready to recapture a city if unable to do so. I find myself sometimes building a wonder that wouldn't otherwise be my current build decision if I didn't need the golden age points. and then there's the decision to try to hold off if I don't need the points for the current age, but potentially lose that wonder to another civ. It can get really tense when you lack 3 or 4 points getting to a golden age and can't find anything that looks like it's going to put you over the top. I missed one by 1 point one time. And then there's the time when the next age doesn't come around as quickly as expected, you end up with 100 point more than necessary [literally, this happened to me] and you worry about how you're going to make the next one since all those strategies you thought were going to have a major effect on the next era are not there anymore.
Zombies and Apocalypse I don't use and don't anticipate doing so until I've at least run through all the updated civs under the new rules and am just looking for something different to play.
So, bottom line, I leave six of them on all the time and never turn two of them on.
