Base Breaker: Karsa Orlong. A Canon Sue in a world of Canon Sues, while also being a Conan the Barbarian expy with vastly more power and fewer redeeming qualities. Oh, and he also rapes people repeatedly in his introduction story (while calling them 'children', though they're adults, due to the difference in size between his race and theirs. And yes, the effect of Hot Skitty-on-Wailord Action is fairly graphically focused on.) And is generally treated as heroic, if brutal. As you might expect, he is slightly controversial.
It is, however, worth noting that Orlong is intended to be a deconstruction of the Barbarian Hero archetype and is not intended to be sympathetic (at least at first), as per Word of God. As for his tendency to rape people, this goes away as he undergoes Character Development. Even fans of the character don't find him sympathetic when first introduced; it's only later in his character arc that he becomes likeable to his fans.
Complete Monster: Bidithal is an elderly member of the rebellious army the Whirlwind and its most powerful High Mage who gets away with his atrocities due to his power and high position. He has a disturbing taste for little girls that he rapes and performs female circumcision on. In his darkest act, Bidithal captures the adopted daughter of the Whirlwind's leader, Felisin the Younger, and rapes her. He tells her he will "drink all the pleasure from your precious body, leaving naught but bitterness, naught but dead places within." Even the barbarian Anti-Hero Karsa Orlong finds Bidithal an utter blot on humanity as a whole and relishes a chance to force Bidithal to choke on his pleasure.
Crazy Awesome: Karsa Orlong, Iskaral Pust, Tehol & Bugg, Second Seguleh, Bauchelain and Korbal Broach, probably all sappers...
As we see in The Crippled God, after becoming Master of the Deck, Captain Ganoes isn't afraid to come to talk to a dangerous enemy commander, just to see what person she is, and piss her off just by talking... and he gets away with it!
Cult Classic: Opinions abound that it will never reach mainstream success circa A Song of Ice and Fire because the depth and complexity that makes it great is alienating to casual readers, and cannot be translated to other mediums.
Cotillion and Udinaas are quite popular. The former quite openly, the latter having a cult following little talked about.
Torvald Nom, who only shows up briefly in House of Chains, has gained a lot of popularity, spawning forum rants about how badass he is . In Toll the Hounds, be becomes an Ascended Extra, with his own minor storyline.
Fandom Berserk Button: The Malazan Book of the Fallen was written by Steven Erikson, not Steve Erickson, Stephen Erickson, or even Erik Stevenson. To add insult to injury, a good number of people who cannot be bothered to take a look at the cover are those who claim he cannot write worth a damn.
Felisin Paran. Sure, she's abrasive and ultimately leads a fanatical rebellion, but she was sold into slavery by her own sister (to protect her from the Malazan Empire's cull of the nobility, but Felisin seems to have regarded it as a Fate Worse Than Death), prostituted herself to protect herself and her friends as a result, lost several of those friends in her escape from the Otataral mines, became the mind slave of an insane goddess who wants to wipe out humanity, and is ultimately killed by the aforementioned sister, who never even realises that she was fighting Felisin. Her whole life is basically one big Trauma Conga Line and ultimately a particularly nasty case of Shoot the Shaggy Dog.
Rhulad Sengar. Yeah, he's technically an Evil Overlord and has done some inarguably bad things- but just look at the rest of this list. You've got to feel sorry for the poor guy. He needs a hug. And possibly, a therapist.
To a certain extent, Kallor. He has very few, if any, redeeming qualities and most of his problems are self-made, but given how much his life has sucked it's difficult not to feel somewhat sorry for him as well.
The Pannion Seer, whose admittedly reprehensible actions are the result of being driven insane over hundreds of thousands of years due to actions of the Crippled God and a K'Chain Che'Malle Matron, plus his own guilt over what he believes to be the death of his sister. When he's de-brainwashed he turns out to be a pretty nice fellow.
Kaminsod, the Crippled God himself, whose long imprisonment would probably have driven anyone mad. All he really wants is to get home. When he's freed he, like Pannion, turns out to be quite nice and actually assists the heroes in saving the world from the Otataral Dragon, not to mention being the narrator of the whole series.
Challice is unfaithful to her husband - it's implied serially - but it's also made plain that this is because she's been cajoled by the strictures of her society and family pressures into a loveless Arranged Marriage with a man who's a bit too much of a Jerkass for her to ever love. She clearly feels trapped by the norms of Darujhistan nobility and it's indicated that the main reason she cheats is because it's the only thing that makes her feel alive. She talks about her plans of escaping, but inwardly she suspects they will never happen. Ultimately, when Darjuhistan comes under siege by Hounds of Shadow, she is so overwhelmed by fear that she ends up killing herself, not aware that her husband has been killed in a duel - by her lover, no less, albeit for reasons of revenge that have little to do with her marriage. Whether she even counts as a jerkass depends on how sympathetic you are to her adultery, but her woobie status is pretty difficult to dispute.
Mayen abuses Feather Witch, and the abuse is heavily implied to be sexual in nature. However, Mayen herself is the victim of rape at the hands of Rhulad, who himself may very well be too insane to realise that what he's doing is wrong at first. He eventually comes to a Heel Realization and both makes Mayen stop her abuse of Feather Witch and frees Mayen of her forced betrothal to him, but by this point she has already crossed the Despair Event Horizon and after being chased by Letherii who apparently intend to rape her is ultimately Driven to Suicide.
Feather Witch also qualifies; her abuse at the hands of Mayen qualifies her for the Woobie part, while her appalling treatment of Udinaas, who is hopelessly in love with her, qualifies for her the Jerkass part. It's subtly hinted at one point that her treatment of Udinaas may be due to her unwillingness to reciprocate his affections, but it's not firmly established one way or the other, even in her internal monologue.
A particularly obvious example, Sirryn Kanar in Reaper's Gale seems to exist solely to cross it repeatedly.
Mallick Rel convincing High Fist Pomquarl to abandon Fist Coltaine to die outside the walls of Aren. Particularly vile since Coltaine was less than five hundred metres away, the garrison was more than strong enough to rescue him and Coltaine had just spent the last few months leading 30,000 Malazan refugees across a desert to safety.
If that's not bad enough, Rel crosses it again only a few pages later when he betrays Aren to the Army of the Apocalypse, resulting in 10,000 soldiers being crucified and left to die.
And the absolute worst part? He's a Karma Houdini, and when his plan fails he convinces everyone that he was the hero who defended Aren and that Coltaine and the Wickans were the true enemy. After Laseen's death he becomes Emperor of the entire Malazan Empire.