For me, playing mostly on Immortal, my go-to is a Domination/Conquest mostly on one landmass, probably Pangaea, probably with Cuirassiers or Cavalry. I don't usually have much patience for Conq/Dom games with 1 movement units (to counter the tedium I've played Small maps, but I find having only 4 AIs boring), but I've done Construction rushes and rifles/cannons before out of necessity. But when I'm tired of the standard style, I get excited to play these other types of games because they feel very different:
- Culture: the strategy with diplomacy feels very different, and there's a lot of Excel-on-second-monitor to figure out how much commerce each of my 3 cities have/will have, where to build the Hermitage, how many Great Artists and where to use them, etc. So much tile micro, play much slower.
- Archipelago (regardless of wincon): feels like a different game, with a vastly different tech path, different buildings in cities, completely different units, etc.
- Playing quickly on Emperor difficulty: Just feels nice not having to micro everything so much
- Rushing the Pyramids and running a Specialist Economy: There's a very specific joy in getting loads of great people, not building many cottages, and then chewing through Classical/Medieval techs in 3-4 turns
- Always War on lower difficulty: Haven't done this, but have approximated it by choking an AI with Quechuas before. Watching Henrik videos it looks like quite a different type of game.
- One City Challenge on lower difficulty: Also haven't done
- Years ago, I played an Epic speed game, which I think honestly is better balanced - tech is much slower so timing windows are much wider. For example, it's much easier to attack with knights before they get longbows. Which means you don't need to plan a war for 1000 years - you don't have to build your whole 5000-year old civilization on ONE timing attack with one or two units to hit a gap before your enemies tech up. But it's just too slow and too tedious, so I never did it again.