For those saying science fiction would cease to exist, I don't think it would. People never stop imagining what will be next.
At what point do you decide you're 'living in the future' and stop imagining? Whatever year you're in, it's always 'the present' and you take what you already have for granted. We have tablet computers, smartphones, ebooks, electric cars, video communication, the world wide web, god knows what else, but we're still imagining. The world of Trek would be no different. They're surrounded by starships and warp drives and wormholes and godlike noncorporeal beings, but this is their status quo. They'll be wondering what's next, just like we are now.
It could be, as
@Tim Walker said, intergalactic travel vs interstellar, or a world where time travel is the norm rather than a relatively exceptional event (bearing in mind that in VGR and ENT we saw glimpses of a future Starfleet that could time travel with ease), 'transwarp' capabilities on every ship, or maybe even ways of travelling that don't involve a ship at all. Or as
@Arpy said, Dark Matter/Dark energy, or deep theological stuff related to the nature of the universe itself... Basically anything that's out of their grasp in the 'present'.