Simple answer. What they do. Actions speak louder than words. I personally like self centered narcissist as bad guys.
A few different things: -- When a character consistently "doesn't get it." Sure, some dramatic irony is good, and can help create tension when used right. But when it's overboard, I just want to scream at the character for not grasping something that seems obvious to me when the clues are right in front of their face. (Unless it's an unreliable narrator, such as a small child or someone who's mentally handicapped, where it makes sense for them to not get it. And I'm not saying that kids and exceptional people aren't capable of picking up on things, but you know what I mean.) -- Characters' actions should be based off of their personalities, and on what that person would do. Sometimes they'll do the wrong things and sometimes the right things, just like us, but a well-developed personality will determine when they make the right and wrong choices, and their actions will seem overall consistent with the character. Too often, I read characters who always do something because it's noble, or just, but they lack development and are just cookie-cutter perfect good guys. It's irritating. -- Characters who believe that the ends justify the means, or that they don't have to respect the rights and liberties and dignities of other people/characters. If this is the villain then great, but I couldn't ever sympathize with a hero with those traits in stories where the author makes it seem right (unless the author portrays it as a flaw, in which case, it's different) -- Characters who only serve as a vehicle for the readers to see the scenes, but who have absolutely zero development -- Characters who are shoved down my throat and act like they're cute all the time when really they are just annoying -- When strong, independent female protags immediately become dishrags (in a way that's glamorized, not treated like a flaw) the second they get the man of their dreams. You can be in love and still be strong and independent. You can become a stay-at-home mom and still be strong and independent. But I hate when romance protags immediately let their guy do all the thinking, talking and acting for them.
When you say detestable, do you mean that the writer planned to have this character hated, or that the character itself is just hated by the readers. If it's the first, I'm with the second poster that it's their actions which make them what they are. If you make them push the boundaries set forth within the story, they might very well become hated in the way that the writer wants you to hate it. If it's unplanned, then it's when the character is badly portrayed or when it becomes out of character. That's a pretty much a generalisation of how I can see characters becoming hated. Being overly dramatic is just a subset of being badly portrayed in my opinion.
When they're completely hollow -- characters written horribly that seem like cardboard and are only used to fill a hole in the plot.
Characters who angst all the time! Makes me want to throw the book against the wall. Alternatively: Characters who do completely idiotic and dangerous things so the author can show how "cool" they are (it's usually portrayed as self-sacrificing and brave- whereas if someone ACTUALLY did do something completely dangerous in full knowledge of said danger; it's usually out of duty or necessity)
When their name matches what they are by circumstance. Like in Harry Potter: Remus Lupin (Remus being one of the founders of Rome who was supposedly raised by wolves, and Lupin having the same root form as "Lupine" which is used to refer to wolves). His parents were just ASKING for him to be attacked and turned into a werewolf. I really hate that. I mean, a nickname makes sense, but yeah... just no.
I love that! There extra easter eggs which all the fans love looking for. Plus Remus is like from Romulus and Remus the twins that were raised by wolves. I personally hate cardboard cut out characters like Bella Swan, who have no personality and are just dull.
Characters that have so many insecurities that they are not insecure but actually have low self-esteem.
OHH... Also, characters that so damn indecisive in their decision making. And even worse, all their problems being multiplied because of that indecisiveness that you spent 3/4's of a book reading about "Oh my, and what if, and but I can't, but I must, but what if he thinks, yes, no, yes, no..." problems until you get to the climax of a the scene and it comes down to her/him makings decision that they shouldn't have made from the very beginning.
I hate characters that are purely created to oppose a stereotype or make a statement. For example, a butch or tomboy princess created simply for the purpose of opposing the traditional pretty princess. It's really obvious when the author does this, because there's making a character quirky, then there's trying to show off your "unique" character, who is really just the opposite of the traditional version we usually read about.
When villains or antagonists are evil simply for the sake of being evil and have seemingly no motivation or background.
"dislike" as in loving-to-hate a terrific villain or antagonist? Or "dislike" as in you want to smack them hard enough to send them flying out of the book you're reading, never to return?
