Now that I think of it, I have never really shipped anyone together myself.
Let's see... I'll try doing this by team to organize my thoughts.
Ruby could work well with Oscar, depending on what happens to the Ozpin part of him. If it eventually fades away/combines with Oscar himself, then it would be fine. But if Ozpin is still there as Ozpin, any relationship would be very awkward.
Weiss... I got nothing. I don't think she would work well with Jaune, at least not yet. Jaune still has a ton of unresolved emotional baggage from Pyrrha, and so he definitely is not ready for a relationship. Weiss also has emotional baggage, but it is a completely different kind so they wouldn't be able to bond over that. I'll just go out on a limb and say Weiss+Flynt.
I think Blake and Sun could work depending on how their relationship plays out, as of now I just see it as Sun being half-obsessed with Blake, while Blake views them as just friends.
I can't think of anyone to ship Yang with. I know some people would say Blake, but I don't see any indication that either of them is attracted to girls. I could potentially see Yang being Bi, but that's a discussion for another day.
*glances at the two Canon ships* I don't think there's much I need to say here.
I completely forgot these guys existed. I don't know enough about any of them to draw any conclusions.
Summer... Wait, why am I discussing how to ship someone who has been dead for at least ten years?
Taiyang seems like he's too settled into his life to even consider a relationship. There's still probably a ton of bad blood between him and Raven because she literally just dumped Yang on him. At best they can resolve their past, but there's no way they're becoming a couple again.
Raven: see Taiyang
Qrow is probably willing to throw himself at anyone who would give him a chance, so I doubt he would ever stay with someone for a long-term relationship. In Chibi, I definitely would ship him with Winter, but in the main show, not so much.
Sun: see Blake
Don't know enough about the rest of the team to comment.
*looks through the rest of the character list*
I'd want someone to ship Ilia with, since I don't like her being alone as the only lesbian so far, but I can't think of anyone. Although I said earlier that Yang could be Bi, I can't really see the two of them working together even if that were the case. The only other girl I could see being attracted to girls would be Emerald because of her behavior around Cinder (which is a borderline complete obsession), but that wouldn't even be remotely a possibility until after a redemption arc for Emerald.
So yeah, that's all I can think of.