This can be anything from Hyperspace in Star Wars, Warp Drive in Star Trek, travel through the Warp in Warhammer 40k or anything else.
I’ve always liked “slow” FTL travel, where going a few light-years still takes a few days or so. I also really like travel through an alternate dimension like in 40k, Event Horizon, Witchspace in Elite Dangerous.
I wanna know your favorite versions, or do you prefer stories that obey the laws of known physics, like the Expanse or Rimworld?
Warp Drive in Star Trek. Largely because there is modern day physics that points to the possibility of it being an actual possibility.
From a story telling, fits into the narrative version, the FTL in the newer Battlestar Galactica series. Look no further than the Battle of New Caprica. That was fracking awesome.
Alcubierre drive, my favorite too
trek also has some interesting non-warp drive ftl. like transwarp, vortex drive, slipstream which is likely resembling hyperspeed/hyperspace. the voth version of transwarp seems quite different from the borg one. they also have non-ship propelled ftl, like different forms of rifts, or teleportation(like subspace catapult system)
i dont really like STD spore drive, and kurtzman practically downplayed the ftl in the later season, he knew it was causing too much criticism for the series, because hes like cheating by inventing a new unknown tech that is absent from the franchise" a secret in the series" to explain the lack of inwarp flight scenes, hence probably why there series isnt so good. a ftl tech/teleportation that is more advanced even 900years later, when they went to future is going to cause alot of problem story and writing wise.