School: Headmaster of Durmstrang
Affiliation: Death Eater (former)
Professor Karkaroff is the headmaster of Durmstrang, a European school of magic with a fairly nasty reputation. In fact, Draco Malfoy boasts that Lucius Malfoy almost sent him to Durmstrang (must be bad, then). Apparently, Durmstrang doesn't admit "riffraff" (11.69) – a.k.a. Muggle-born witches and wizards – and it also teaches Dark Arts, rather than just Defense Against the Dark Arts. Professor Karkaroff is an old acquaintance of Lucius Malfoy's, a sure sign that he was once a Death Eater. So, even before we meet Karkaroff for the first time, we have a fair idea of what he's like.
Once the Durmstrang students arrive to start the Triwizard Tournament at Hogwarts, we finally get to clap eyes on Karkaroff. All of the adjectives J.K. Rowling uses for this character leave an impression of insincerity: he has a "fruity, unctuous voice" (15.146) ("unctuous" meaning (in this context) oily or greasy) and a flattering, sly manner. Karkaroff doesn't look or sound trustworthy from the get-go.
In fact, Karkaroff's unreliability goes both ways: he's not just insincere with good people; evil people also find him unreliable. We later find out from Dumbledore's Pensieve that Karkaroff willingly named the names of all of his Death Eater friends to try and get a shorter sentence in Azkaban Prison for himself once Voldemort fell. Sirius comments that, "Karkaroff doesn't strike me as the type who'd go back to Voldemort unless he knew Voldemort was powerful enough to protect him" (19.156). By the end of the novel, Karkaroff flees Hogwarts because he knows Voldemort has risen again: "he betrayed too many of his fellow Death Eaters to be sure of a welcome back into the fold" (36.153). Karkaroff is so slimy that neither side can trust him, good or evil, and he winds up having to run away to save his skin from his own former master, Voldemort.
Karkaroff spends most of his time at Hogwarts trying to make sure Viktor Krum wins the Triwizard Tournament. Whenever Harry does very well on a task, Karkaroff gives him an insultingly low score so Harry doesn't get an advantage over Viktor in the competition. And when Karkaroff hears that Mr. Crouch (a Triwizard judge) appeared near Harry and Viktor and then apparently disappeared after Stunning Viktor, Karkaroff accuses Professor Dumbledore of rigging the tournament. (Hagrid almost rips his head off after that accusation.)
Karkaroff also spends a fair amount of time pestering Professor Snape. As the Dark Mark grows clearer and clearer on his arm, Professor Karkaroff starts haunting Professor Snape's classroom and asking what he should do. Snape tries to hush Karkaroff up, but he's in such a panic that he doesn't bother being subtle about waving his left arm around. All of Karkaroff's theatrics make Harry and Sirius suspect that Karkaroff might have put Harry's name in the Goblet of Fire. But, it turns out that Karkaroff is more afraid of Voldemort than Harry is, at this point.