I've just got back from Catherine's birthday dinner and I am stupidly sleepy and overworked, but since today's question was a pretty easy one, I'm going to squeeze in an answer before I go to bed.
My "pairing I will never understand" is Sheldon and Penny from The Big Bang Theory. I just don't see any kind of chemistry or UST between the two, and other than an alternate universe episode, dreamscape or something like that, I actually cannot believe people actually ship this couple. What show have they been watching?? Sheldon is a sociopath with OCD, he has trouble with the most basic of human relationships (family, friendship, coworkers) and people would like to see him in a romantic relationship? Do they realise how impossible this is? Especially as he does not like physical contact and is terrified of germs? So, despite the fact that these two are funny, they don't have to be funny in a romantic kind of way. They can be cute as friends. They must be cute as friends. To turn it into anything else means to completely negate the whole show, and I don't think they'd ever be so stupid!