I suppose at the very least odious characters are memorable. I've written about them already here and here. For me, it is always a thin line between characters who are driven by some monomania (Captain Ahab but also Ignatius J. Reilly) and who cause others around them distress or even pain through their thoughtlessness, and those who intentionally hurt others, sometimes out of spite but sometimes just out of boredom (Rebecca Sharp does come to mind). I suppose it is true that there aren't too many leading characters that seek to physically harm others (particularly in first-person fiction), though there is A Clockwork Orange...
Looking just at the first-person fiction, there is a noted phenomenon where readers do tend to be more forgiving of characters written in the first person, since there is a collapsing of the distance between reader and character. Quite a few authors have played around with this and sort of pushed the envelope in terms of just how far they wanted to go with "special pleading" on the part of their narrator, justifying some pretty terrible behavior.
Sometimes it is just the story of a character who is barely in control and may actually have quite a bit of internal turmoil (or even self-contempt), which leads him or her to drink too much or take too many drugs, and then lash out at those around. I would generally lump Barney Panofsky from Richler's Barney's Version in this category. I found him pretty unlikable and am quite sure I would have cut him out of my life, and not kept accepting his various excuses for why he had behaved so badly.
I'd forgotten how badly Joseph, the narrator of Bellow's Dangling Man, acts. No question the strain of being in a terrible position (just waiting for the army to straighten out his enlistment papers but unemployable in the meantime) has gotten to him, but he still acts beastly towards others that are trying to help him out. I've just never really cottoned to characters who refuse financial assistance or even charity from others out of some stiff-necked pride when their families are in trouble. That completely turns me off, particularly when they then go on and on about it, crowing about how noble they are not to have to stoop or dissemble for a hand-out. It is a totally false, misplaced pride. (While I also dislike the fecklessness of characters who cannot be bothered with monetary issues like the mother in Molly Keane's Good Behaviour or pretty much everyone in The Cherry Orchard, this is still easier to take than harming one's family through misplaced pride.) Even here it is a fine line. Being overly and unjustly proud probably makes for an unpleasant and probably foolish and possibly tragic character, but not necessarily an odious one. But Joseph definitely crosses that line. He creates scenes in restaurants and then, while visiting his brother's family over the Christmas holiday, gets in a row with his niece and spanks her when she insults him. He's really a piece of work.
There are more than a few parallels with Mickey Sabbath from Philip Roth's Sabbath's Theater, including sneaking around in a girl's room and generally reeking of self-pity. While Bellow buries the sexual connotations (not very deeply it should be said), Mickey Sabbath practically glories in his perversity. The scene I am referring to has Sabbath coming down to Manhattan for the funeral of an old friend. He is staying with another friend who tries to clean him up (figuratively and literally). He then prowls through the girl's drawers, looking for underwear he can use to inspire him during a masturbation session. He also fantasizes about having an affair with his friend's wife, and I think he tries to screw the maid, as well, but I can no longer remember if he is successful. I'm fairly sure this scene is Roth's riff on Boudu Saved From Drowning, but it doesn't make it any easier to swallow. (There's something about ingratitude that rubs me so much the wrong way that I haven't decided if I will ever watch Boudu, despite all the raves it has gotten over the years.) Anyway, Roth doesn't stop there, but later in the novel (after being expelled from his friend's house and returning to New England) has Sabbath jerk off over his dead lover's grave a few times as a tribute. What a guy...
I guess the best that can be said about such train wrecks as Joseph or Mickey or even Ignatius is that their antics mostly hurt themselves, though they often let down people around them who may still care about them.
There is another type of character who contributes to harming others, though it may be expressed as keeping some minority group in its place. In almost every case I can think of, the author is trying to make a point about how racism works (and isn't condoning the actions of the racist characters). That doesn't necessarily make it any easier to read about these acts. Perhaps the most clever move is to write a first-person story about a reasonably intelligent but still actively racist character and subtly point out how their racism harms themselves as well as others, in addition to leading them to violate their own principles time and again. This was handled very well in Ivan Vladislavic's The Restless Supermarket.
I'm finding Gregor von Rezzori's Memoirs of an Anti-Semite to be very much in the same vein, though Rezzori cuts a bit deeper here, essentially claiming that pretty much all of the attitudes of the elite Germanic types from 1890s through 1930s were backwards and racist and useless for modern life. In this book at any rate, I'd say the critique of Aryan-ness goes much further than Gunter Grass goes for example. In this case, Rezzori may pile it on just a bit too thick to the point that, despite being written in the first person, I've gotten quite tired of the narrator and his obsession with Jews. I definitely liked An Ermine
in Czernopol better.