This one is again prompted by fanfic searching. I'm not going to discuss slash or femslash pairing because we all know I prefer het. I'm going to list some het pairings (many apparently popular) that I just cannot get into.

Avengers (MCU) -
Loki/Anybody - Sorry, but Loki is a villain. I cannot see him with any of the ladies of the Avenger MCU. His actions put all of them in danger and directly affected a handful of them. To pair them with him? Even if he were to really, really repent and turn his life around, I just can't see it.
Clint/Natasha - They are too much alike - something or someone is needed to balance them out. It's the dark shadows inside both of them - without someone or something light to help offset that, I can only see their story going dark and I like happy/hopeful endings.
Coulson/Hill - Again, too much alike. Both of them are scarily efficient and stoic. They need a lighter note or a crazier note to work. It's one of the reasons I can get behind Phil/Darcy or Phil/Pepper (if it didn't break up OTP's) - Darcy provides crazy while Pepper is light. For Hill, I either can see her with Steve or single.

Buffy -
Buffy/Angel - the Romeo & Juliet of the Buffy-verse! Can't stand it. He's over two hundred years old and acting like an untried teenager! Also - while they should embody the 'opposites attract', the truth is that they are too much in the same world, and its a dark one.

Firefly/Serenity -
Jayne/River - no, just no. I can see them finding a happy medium, but I don't think the two of them would ever make a decent pairing. Jayne is too much the merc, even with his moments of heroics, and River has been badly damaged by people who concentrate too much on the end result and not enough on the people.
Simon/River - ICK!!! Please see my entry on incest.
Mal/Zoe - Nope...I think this is one of those partnerships that would not grow with a romantic/sexual relationship, but that would actually die.
Mal/Inara - I know this was a canon thing, but I'm sorry, I didn't like the relationship between the two of them. Neither really accepted the full person - Mal didn't really accept Inara's profession while Inara didn't accept his shadows.

Glee -
Finn/Rachel - they brought out the worst in each other, but most of all, Finn made Rachel a weakling instead of the strong 'go for the stars' person she could be. It probably doesn't help that I didn't care for Finn and thought he got away with stuff nobody ever let any other character get away with.
Puck/Quinn - too much bitterness here...too much history - to try and make it a pairing just seems like trying to fit puzzle pieces that almost work, but not quite.

Harry Potter -
Ron/Hermione - one of JKR's end games, but I couldn't see it. I'm a believer in the 'opposites attract' thing, but there has to be something other than death, danger, and destruction to draw people together. The two of them only seemed to have Harry and fighting Voldemort as common ground and I couldn't see it.
Harry/Ginny - I could see this one better in the movies, but in the books it seemed really forced. I think it had been developed better, I might have liked it.

Leverage -
Hardison/Parker - Again, canon - again, I don't ship it. Both of them, to me, seem the flightier members of the team. They're the least serious really, and I think Parker, at least, needs someone to ground her, someone who can give her a foundation.

Stargate Atlantis -
Rodney/Jennifer - This one is one of my dislikes that I can defend the least. While I adore Rodney, I just don't agree with Jennifer's choice.

Feel free to ask any other opinions!