When Nepeta starts adding the humans to her shipping charts, she puts Dave/Tavros as a likely red couple.
In the afterlife, Tavros specifically seeks out Dave (from a doomed timeline) for eternal companionship, to Dave's annoyance and Aradia's amusement.
Dave and Karkat, starting here. Karkat tries to organise their dating schedules so they can both have Terezi, which Dave thinks is incredibly presumptuous since Terezi knows nothing about this. They end up grappling over a pen and scribbling all over the book Karkat is using, drawing penises all over the page, and wrestling on the floor while Kanaya and Rose look on.
KARKAT: YOU DON'T EVEN UNDERSTAND THE SOCIAL IMPLICATIONS OF ALL THIS HOSTILE TOUCHING AND GRABBING DO YOU???
Check out Kanaya's reaction ... if it went on for another ten seconds she would start auspicitizing them.
Roxy, Jane, and UU. UU calls Jane lovely and Jane is willing to believe what she says about SBURB because UU is so nice to her. Jane and Roxy have canon Ship Tease; in the reprise of [S]: Ride, there is a picture of the two kissing (cut off above the waist) and uu has requested art of the two of them together. Roxy tells UU that she loves her, and UU mistakes this as being literal. But Roxy does state that she has conciliatory feelings for UU, and UU tells Roxy her name in the hopes that if she never wakes up on her own, Roxy will be able to do it for her. To which Roxy responds that she'll shout UU's name into the Void until she returns.
Dirk is canonically queer, although he chooses not to label himself. He's spent most of the story so far being enamored with Jake. The two eventually start dating after entering the Medium. They're currently broken up, though.
Jake possibly identifies as bisexual. There's no denying his love for blue women and Lara Croft, but he decided that out of all his friends he would be the most compatible with Dirk.
He still has a dream-mind Dirk around to comfort him even after they broke up.
After powering up, he made Brain Ghost Dirk become real. BG!Dirk refers to Jake as his boyfriend, which may mean Jake still has feelings for Dirk.
All the trolls seem to be pansexual, and most have been in relationships with both sexes. The concept of only being attracted to one sex is completely alien to them.
Although Word of God states that, despite this, Kanaya is a lesbian.
Rose and Kanaya are currently dating, and have been for some time now.
Rufioh and Horuss are basically a troll parallel of the Dirk/Jake relationship.