Vulcans blame humans for being so emotional and illogical, yet, as demonstrated in episodes like "Amok Time" and "Take Me Out to the Holosuite", there is nothing logical about their own contempt for humans.
Also, the Vulcan motto is "Infinite Diversity in Infinite Combinations", just so long as you think and behave exactly according to the rules that one man wrote thousands of years ago, and don't you dare pollute our precious Vulcan purity by adopting or breeding with offworlders, you filthy race traitor.
Star Trek: Enterprise and several novels in the Expanded Universe have gone on to explore Vulcan culture in considerable depth, and one of the key facts about the Vulcan ideal of logic and rationalism is that it is just that, an ideal. Not many Vulcans actually live up to it, and a non-trivial percentage manage to come up with totally "logical" (to themselves) justifications to be arrogant, self-righteous, and bigoted.
Klingons are brave and honourable. Except when they're not. Later seasons of Next Generation and Deep Space Nine made it very clear that "honour" among Klingons was the exception rather than the rule: most of them were nothing more than thugs or bullies, many of them were deceitful and treacherous, their leadership was riddled with corruption and they were more than happy to cover up acts of extreme dishonour out of political expediency. We can only hope that Martok made some significant changes. This is at least partly a translation issue; with the exception of Worf what Klingons mean by 'honor' is the old-fashioned reputation/face kind, not the internal code kind.
Troi gets called out on her hypocritical attitude regarding use of Betazoid empathy during the third season episode The Price by her love interest of the week, Ral. When she complains to him about his use of empathic abilities to gain an advantage at the negotiation table, he flatly points out that people have done such things for thousands of years without anyone calling foul while he simply happens to be slightly better at it. He then goes on to point out the real hypocrisy as he sees it: Troi uses her empathic abilities every bit as much to aid her 'client:' the crew, the captain and Starfleet, often at the expense of whatever opponent they're dealing with at the moment. As Ral states, the difference between them is that when Troi manipulates and spies on the opposition without their knowledge or consent, people very well might die rather than simply fail to acquire some property. Troi's arguments are supported, however, by the implication that Ral is directly influencing his opposition during the negotiations, and using his empathy to manipulate them into dropping out of the race entirely.
The Cardassians led a brutal occupation of Bajor, and are later themselves occupied by the Dominion. It leads to this exchange between Damar (a Cardassian) and Kira (a Bajoran) when Damar learns the Dominion has executed his family:
Damar: To kill her and my son... the casual brutality of it... the waste of life. What kind of state tolerates the murder of innocent women and children? What kind of people give those orders? Kira: Yeah, Damar, what kind of people give those orders?
Doubly hypocritical given Damar himself has casually murdered an unarmed woman (Ziyal). She might, by her own admission, have been an enemy of the state, but at the time she was no threat and could have easily been subdued.
Notably, this is actually part of his character development. Damar toed the line under Dukat and the Dominion, slowly being driven to rebel after seeing his people be pushed to the sidelines and sacrificed needlessly. It is this quote that helps him to realize what Cardassia was, and why it needs to change. Garak even pointed this out to Kira when she regretted her words, telling her that if Damar would lead a new Cardassia, then Damar's pain made him more receptive to Kira's words, not less.
Gul Dukat became a leader of a Pah-Wraith cult and tried to lead them in a mass suicide. While holding their suicide pills, Kira tried to stop them and bumped into Dukat and the pill he was holding became scattered with a few hundred others. The cult got Kira under control but Dukat was frantically looking for the pill he had. Everyone realized that his pill was a fake; he wasn't planning on committing suicide at all. Needless to say, his influence on the cult fell apart pretty quickly. Though one cultist did take the pill anyway even after Dukat's lies had been exposed. Dukat claimed that the Pah-Wraiths had told him to take a fake pill and get everyone else to kill themselves, and the cultist in question decided to believe him, even if he didn't seem to like it. It should be noted, also, that this might not be hypocrisy at all — the Pah-Wraiths are essentially the Legions of Hell, posing to the cult as misblamed fallen angels when in actually they are Omnicidal Maniacs- it is could be that they really ''did' order him that which would mean he isn't actually a hypocrite (in this particular instance, at least).
Garak spends a lot of time complaining about Bashir's Federation smugness, and a similar amount of time extolling the cultural superiority of Cardassia.
Vulcan captain Solok has built his entire academic career on the assertion that Vulcans are inherently superior to humans and other emotional races, but he's the one who refuses to let one Academy incident with Sisko be forgotten, to the extent that he teaches his crew baseball. There's certainly no logical reason for him to pick baseball and then challenge Sisko except that he wants to humiliate Sisko, and there's no logical benefit for him to do so. When the Niners celebrate getting one run as though they've actually defeated Solok's team, Solok's pissiness at their "incorrect" reaction has them pointing out, quite correctly, that he's getting embarrassingly emotional about the matter. He's also still ranting about "human" emotions when most of the Niners aren't human.
The Borg Queen - the body and voice of the Borg Collective - is dismissive of how Voyager helped Seven regain her individuality, and comments to Seven "they've taken you apart and recreated you in their own image." You know, like Borg assimilation does to individuals the Borg have taken.
Captain Archer is prone to excessive hypocrisy, to the point where many viewers saw him as being written as a case of Protagonist-Centered Morality.
Contrasted in the episodes "Dear Doctor" and "Observer Effect". In "Dear Doctor", the Enterprise makes contact with a race of aliens that are dying from a genetic disorder which, according to the Goal-Oriented Evolution cited by Dr. Phlox, they "evolved" so as to make room for another species on their planet with more evolutionary potential. Although Phlox can provide a cure, he and Archer agree to not help the aliens, observing that they don't want to "play God" and that in the future there may even be a rule about this (i.e. the Federation's Prime Directive). But in "Observer Effect" Trip and Hoshi return to Enterprise having contracted an incurable disease while digging around in an alien garbage dump without hazmat suits. They soon die and Archer at least has also become infected as well. It turns out that a couple of Sufficiently Advanced Aliens have been watching this all play out. Both Phlox and Archer blast them for their complete lack of compassion. Archer goes even further, referencing his decision in "Dear Doctor", but not accepting it as an excuse for why these aliens have not intervened to help him and his crew with a disease they contracted through sheer carelessness.
Archer's actions in "Fortunate Son" where he tirades against Ryan for seeking revenge against pirates who have repeatedly attacked his ship and nearly fatally injured one of his crew, compared to "Silent Enemy" where Archer seeks revenge against unknown aliens who have repeatedly attacked his ship and nearly fatally injured one of his crew. Bad enough already, but the latter takes place only two episodes later!
During this same argument, Archer states that Ryan cannot be a vigilante while at the same time acknowledging there is no such thing as organized police in this part of space. Queue Archer running around with an armed ship doing whatever he feels is right one episode to the next.
To be fair to Archer, one of his objections to Ryan's actions was that he risked escalating the current tension between Ryan's target (Naussican pirates) and haulage freighters like Ryan's into a more open warfare where the Naussicans would actively destroy other ships rather than just steal cargo. By contrast, in "Silent Enemy" Archer is responding to an aggressive first contact from a position of strength to prevent humans becoming targets from similar threats.
On a more broad scale, Archer is always advocating open-mindedness and embracing other lifeforms, and yet as the series goes on, we find that he falls into the occasional habit of being suspicious, paranoid, and almost hostile upon first contact with truly alien forms of life or humanoids that are very different from the human norm for absolutely no good reason (except maybe his "feelings"), while he is warm, welcoming and forgiving to more familiar humanoids for the exact same lack of reasoning. Sometimes his paranoia ends up being justified. He really edges onto What Measure Is a Non-Human? in his interspecies treatment.
Of course, a sizeable portion of the non-humans he encountered in the third season in particular were the Xindi race who were introduced killing seven million people on Earth, so Archer wasn't unreasonable in being hostile towards them.
Archer's grievances against Vulcans are that they "wouldn't let humans stand on their own feet" and he holds a personal grudge against them for withholding their technology so his father didn't live long enough to see his life's work completed. It never seems to occur to him that by withholding their technology and forcing humans to invent it themselves, letting humans stand on their own feet is exactly what they did.
In "The Breach", Phlox points out that Denobulan Medical Ethics prevent him from treating someone who does not want to be treated and that he must respect his patients' wishes, even if they lead to their death. Which makes his actions in "Dear Doctor" even more shocking in retrospect, since the Valakians most certainly did want to be treated!
Purposefully invoked and deconstructed in "Damage", where Archer realises that in order to reach Azati Prime in time to prevent the Xindi from destroying Earth, he must engage in piracy and steal a replacement warp coil from the Illyrians. In other words, become no different from the Osaarian pirates from "Anomaly" that he so despised.
John Paxton, the leader of the xenophobic Earth organization Terra Prime. He had unwavering dedication to his cause and was willing to scorch half of San Francisco to make his demands known. Considering this was after a devastating alien attack, their concerns about an alien alliance had some validity. T'Pol deduced from a trembling hand that Paxton had a genetic disorder, one that should have killed him when he was a teenager, but didn't because of "freely given" alien medical technology. Paxton will only admit that he's not the first leader to fail to live up to the standard of an idol (in his case, a mass murderer from Earth's post WW3 period), and refuses to back down. This fact exposed him as a man who was just racist.
Movies:
Star Trek VI: The Undiscovered Country: Kirk and his senior staff dine with the Klingon Chancellor and his advisors. The Chancellor's daughter derides the Federation as a "homo sapiens-only club," even though the Federation is made up of over a hundred member races with equal standing whereas the Klingon Empire exercises hegemony over its non-Klingon worlds. In addition, Spock is a Vulcan, and is a captain, serving as executive officer of the Federation's flagship. How many times have non-Klingons been shown serving in equal capacity on IKF starships?
Star Trek: Nemesis: In the TV show, Picard gives long speeches about the sanctity of the Prime Directive and was even willing to let a whole planet die rather than violate it. But in this movie, he casually and fragrantly breaks it when given the chance to do some off-roading with a dune-buggy, firing on the primitive natives with energy weapons and flying spaceships in plain view.
Similarly in Star Trek: First Contact, Picard is absolutely fanatical about his hatred of the Borg due his times as Locutus in "The Best of Both Worlds". This unintentionally makes Picard look hypocritical since in the TV show he was all about to giving every creature a fair shake and even showed mercy to the Crystalline Entity, despite the fact the Entity killed as many people as the Borg did and in its first appearance actually fled like some kind of Dirty Coward after its ally Lore (Data’s Evil Twin) was defeated. But the Borg? Picard hates and kills them with impunity because they hurt him in particular by assimilating him into Locutus and setting him against the Federation.
That said, characters do call him out for his attitude towards the Borg threat, helping him acknowledge that his personal history with them is clouding his judgement.
