Man, the 'Labyrinth' fandom runs on a few key ships, but Jareth/Sarah is the undisputed king. It's wild how much fic is generated from that one dance scene and the 'you have no power over me' line. People love exploring the 'what if'—what if Sarah had said yes, what if Jareth wasn't just a Goblin King but something more, what if he came back years later. The age gap thing gets talked about a lot, obviously, but most fic writers just age Sarah up or handwave it with 'fae immortality' logic.
Beyond that, you see a decent amount of Sarah/Hoggle, which is way sweeter than you'd expect. It taps into that loyal-friend-turned-something-more vibe, and it's often used to explore Sarah's kindness versus Jareth's trickery. Sarah/Toby is strictly a gen thing, obviously, just sibling fluff. I've seen the occasional weird crossover where Jareth ends up with someone from 'The Dark Crystal' or 'The NeverEnding Story', which makes a twisted kind of sense.
The real niche stuff, though, is the rarepair content. I stumbled on a Jareth/Sir Didymus once that was bizarrely poignant. Mostly, the fandom orbits Jareth and Sarah in endless variations—enemies to lovers, slow burn, straight-up smut, fix-its where Sarah becomes Goblin Queen. It's a testament to how powerful that dynamic is, even decades later. The other characters mostly get used as supporting cast to that central pull.