From an "aesthic" point of view: Ifrit and Zurvan. Both are those rather boring, red-black demon-like things. As some others I really liked the FFX-design of Ifrit, even though, thinking about it now, almost no other one (that I can recall right now).

Gameplaywise: Bismarck. Even though I think they messed up Ravana even more, seeing how thats actually a fight with mechanics, that could be so easly skipped however that people were doing that 2 weeks after laucnh (and yes, thats exaggerating, but my point it: even though I've played through all of HW and did the fight relatively early, I only had to do the mechanics once - after that... all skip.
For ARR its probably Leviathan with the whole "press this button in time"-thing - specially because you have to wait for the aether to charge. Granted, less of a problem when the fight was current, hella annoying now.

Music: Zurvan. Mostly because I was extremly disappointed that they were no vocals - dont get me wrong, I like the all instrumental pieces, but they make the songs with vocals really stand out and I liked both Sephirot and Sophia a lot for those vocals alone and was eager to hear what they'd do for Zurvan... and then it was... nothing.

Most annoying to farm: For me that was Ramuh - he didnt wanted to give me his freaking pony and was almost impossible to beat in PF-groups, eventually my static farmed him for me and everyone made very sure that I got the first pony that dropped after they had witnessed me spiraling into despair and madness after three weeks of PF/DF-Ramuh.

Back when I was a little newbie, I was scared of Titan and he would have been my least favorite primal - hands down. Such a stressful fight with my connection- and skill-lag... and his weapons are still some of the most ugly ones in the game (depending on the job). I have to admit that I'm also not to fond of his general design.