I think the first beta ships ride the not so rare/rare pair line very harshly some times so:
Grimdorks and Davejade are the givens.
Trollcops? Remember that ship? I still love it, Terezi and Sollux should've been so pale for each other, they would've had so many fun interactions.
I've developed a spot for red karezi, and since I still adore red katnep, so...red karneprezi?
I also love to see me some sollux<3<karkat
I also also think JaneDave is fun >:0
Although I can't say I ever shipped it myself I think that the entire time the fandom went through the kayana<>karkat ship for years was both incredibly cute, and also funny for reasons I won't explain ever.
HC: There are twelve main classes Muse, Seer, Knight, Witch, Rogue, Heir, Page, Thief, Mage, Prince, Bard, Maid, and Lord---
YN:[yeah dude. Sylphs are fucking gay.].
HC: Shut up!