Worf:"Brother, it is you who does not see. You look for battles in the wrong place. The true test of a warrior is not without. It is within! [points to his chest] Here! Here is where we meet the challenge! It is the weaknesses in here a warrior must overcome!"
Captain Picard had this scene in the episode "The Defector" where he owns Romulan commander Tomalak rather magnificently. Tomalak and his two warbirds have found Picard and the Enterprise on the wrong side of the Neutral Zone. Tomalak demands that Picard surrenders. Picard instead sees his two Romulan warbirds...and raises him three Klingon birds of prey. They could fight, but it would cost Tomalak more than he'd gain and he lets them go.
The scene in the same episode where he just lays into Admiral Jarok after he refuses to give up official secrets:
Picard: You already betrayed your people, Admiral! You made your choices, sir. You're a traitor! Now if the bitter taste of that is unpalatable to you than I am truly sorry. But I will not risk my crew because you think you can dance on the edge of the Neutral Zone. You've crossed over, Admiral. You make yourself comfortable with that.
You've got to give props to Admiral Jarok. The leader of a thousand massacres, including Khitomer, and one of the most important individuals in the Romulan empire... And he turned his back on everything he knew, betraying his own people, because he realised the life of his baby daughter was more important than winning a galactic war based on prejudice.
"She will grow up believing her father was a traitor... but she will grow up."
—-> According to Star Trek Online, not only does she do so, but she ends up in command of the Romulan Republic FLAGSHIP
Picard luring two Borg drones into a Holodeck with its safeties switched off and gunning them down with a Tommy gun in First Contact. This scene was both incredibly Bad Ass (with a sharp white suit) and provided some very scary Foreshadowing of Picard's Ahab moment. AAAAHHH!
In the face of constant, excruciating pain, completely powerless, almost not even able to stand after days of brutal torture, Picard is capable of a Patrick Stewart Speech. Gul Madred tries to play an empathy card to get Picard to be more amenable, talking about how his childhood had shaped him. Picard, barely able to form a coherent sentence, tells Madred that he pities him, and that from now on, all he'll see in Madred is a scared, hungry little boy. Madred is visibly upset and starts hurting Picard, who continues to say it in between gasps of pain.
The crew of the Enterprise-C knowingly went to their deaths. They knew that returning to face three Romulan warships was certain death. They did it anyway, and their courageous sacrifice ensured peace between the Klingons and the Federation... just as it did in the original timeline.
In "Unification I", Picard is trying to arrange a cloaked ship from Gowron for an undercover mission in Romulan space. Gowron is busy re-writing history to downplay the Federation's involvement in his ascension, and Picard eventually gets a hold of B'Ijik, a low-level official. B'Ijik asks Picard what the Klingons would get out of this.
Picard: The only benefit to the Klingon Empire would be our gratitude.
B'Ijik (skeptically): That is what you want me to tell him?
Picard: Yes. And, please add that, if he is unable to provide us with a ship, then I am sure there are others in the Klingon Empire who would be willing to help me. And then they would have our gratitude.
Ah, heck, Spock just turning up at the end of "Unification I" is Moment of Awesome in itself.
In "Unification II", there is a Moment of Awesome for Picard, Spock and Data but an equivalent Crowning Moment of Stupidity for Commander Sela, when after threatening the three of them with death if they don't do what she wants, she * LEAVES THEM ALONE IN THE ROOM* while she wanders off to attend to her plans. What kind of loon leaves one of cleverest and most resourceful Captain in the Federation, a Vulcan of decades of experience, and an android with vast knowledge and incredible physical capabilities, alone in an office filled with electronics and other goodies, without watching them? Come on, tie them to the chairs, gag them, and then assign 3 armed guards apiece with orders to kill them instantly if they make a wrong move, and then you have merely reduced the odds to slightly less than certainty that they will still defeat you!!! But watching the three of them in action practically defines pure awesomeness.
There are Picard's moments when he kicks butt in the legal and diplomatic spheres:
In "The Measure of a Man" when Picard is on the defense hearing to determine whether Data is considered property and goes on the counterattack. He asserts that this hearing would determine whether the Federation is capable of making a leap of a moral imagination to realize Data is a sentient being by most meaningful criteria and to rule him property is to sanction slavery. The fact he wins the argument by opening the eyes of the Judge to this innovative expansion of moral principle is a crowning moment where Picard shows why the United Federation of Planets is worth fighting for.
Picard: Your Honor, Starfleet was founded to seek out new life; well, THERE IT SITS!
He was going up against Riker's Moment of Awesome. Forced into the role of prosecutor by the overseeing JAG officer (who would have ruled summarily against Data if he hadn't accepted), Riker does a damn good job in that role, much to his own dismay. Picard later confided to Guinan that "he almost convinced me."
Riker: Data is a physical representation of a dream, an idea conceived of by the mind of a man. Its purpose? To serve human needs and interests. It is a collection of neural nets and heuristic algorithms. Its responses are dictated by an elaborate software program written by a man. The hardware was built by a man. And now a man will shut it off.
Flips Data's off switch
Riker: Pinocchio is broken. Its strings have been cut.
Guinan: Consider that in the history of many worlds, there have always been disposable creatures. They do the dirty work. They do the work that no one else wants to do because it's too difficult or too hazardous. And an army of Datas, all disposable... You don't have to think about their welfare, you don't think about how they feel. Whole generations of disposable people.
After she says "Whole generations of disposable people", she pauses and just takes a long, slow drink from her glass. In that moment, she shows that she knows she's made her point.
The end of the ep has Data's great moment. Riker is feeling despondent about betraying a friend, when Data comes to get him. Riker is ashamed at his part in the trial. But Data, showing one of humanity's more positive traits, understanding, invites him to the victory party anyway, stating that Riker did what he had to do. Thus showing that Data is in fact deeply grateful for the sacrifice Riker made. Sadly, this was a military hearing and thus did not set legal precedent in either the status of civilians or civil court cases, as Lal and the Doctor discover. It set a precedent for Data, who would use this episode as the basis for his insubordination in the season 6 episode "The Quality of Life", in which he refuses to order machines to their destruction to save Picard and LaForge, because they have demonstrated sentience. Standing up to his superiors on that moral ground, even to the point of being at risk of court-martial, took courage. Even Picard compliments him later that his actions as "the most human thing" he had ever done.
Picard: Order a man to hand his child over to the state? Not while I am his captain.
In "Ensigns of Command", Picard opposes the arrogant and oppressively legalistic Sheliak, who flog the treaty between them and the Federation and refuse to compromise on the matter of an unexpected colony on a planet Sheliak want, but cannot be moved for weeks. By searching the treaty, Picard finds a way to outmaneuver them and makes them sweat. When he knows he's got the Sheliak on the ropes, he terminates communications and waits for them to call back. Once they start hailing, he stands around letting the hailing tone sound, then casually walks across the bridge, checks the Enterprise commissioning plaque on the wall for dust, and finally wanders back to the center of the bridge before putting them onscreen. The closest Picard has ever gotten to "You know what? Fuck you." in the entire series.
Riker: You enjoyed that.
Picard: You're damned right.
In "The Drumhead," Picard puts a particularly nasty admiral in her place and exposes her as the paranoid witch hunter she is after being put on trial by her by quoting her father on the subject of curtailing life's liberties for the sake of the "greater good" just to piss her off and goad herinto a rant.
Picard: There are some words I've known since I was a schoolboy. "With the first link, the chain is forged. The first speech censored, the first thought forbidden, the first freedom denied chains us all irrevocably." Those words were uttered by Judge Aaron Satie, as wisdom, and warning.
In "The First Duty", Picard finally gets his own back on Wesley Crusher when he suspects him of covering up the death of a cadet in a training accident. He beats him down in true Picard style:
Picard:The first duty of every Starfleet officer is to the truth, whether it's scientific truth, or historical truth, or personal truth! It is the guiding principle on which Starfleet is based. If you can't find it within yourself to stand up and tell the truth about what happened, you don't deserve to wear that uniform.
"The Enemy": The Enterprise is facing down a Romulan warbird which has every reason to blow them out of the sky, and with the shields up Picard's losing his chance to rescue his officer and the second Romulan whose presence would stop the imminent battle. He opens a channel to the enemy ship, says basically "We've both got powerful ships and well trained crews ready to die for this, but the only way we're going to avoid starting a war is by trusting each other" and drops the shields. In front of a fully armed Romulan warbird. His engineer is rescued, the return of the Romulan officer avoids a battle, and two enemies move one small step towards peace. All it took was one quick speech and balls the size of a planet.
"The Wounded": Fellow Federation Captain, Benjamin Maxwell, is convinced the Cardassians are up to no good, and nearly starts a war by attacking a Cardassian convoy with his own starship. Picard is ready and willing to fire on Maxwell's ship to keep him from attacking again, and only because O'Brien can talk him down from destroying the Cardassian ship does the situation end peacefully. Then, right when the Cardassian representatives turned to leave, Picard delivers this bomb:
Picard: Maxwell was right. Those ships weren't carrying scientific equipment, were they? A 'research' station within arm's reach of three Federation sectors? Cargo ships running with high energy subspace fields that jam sensors?
Gul Macet: If you believed the transport ship carried weapons, why didn't you board it as Maxwell requested?
Picard: I was here to protect the peace, a peace I firmly believe is in the interests of both our peoples. But if I had attempted to board that ship... I am quite certain that you and I would not be sitting here now. And that ships on both sides would be arming for war. ... Take a message to your leaders, Gul Macet. We know. We'll be watching. We'll be ready.
Also from "Ensigns of Command", Data convincing the colonists (who would rather fight) to leave by practically destroying their colony with a single phaser. He then brilliantly explains that the Sheliak are far more powerful than he is and that the colonists would have no chance whatsoever.
Data: (After zapping the guards) "That was the stun setting. This is not."
"The Best of Both Worlds" had (at least) one for both Picard and Riker that would define the season-ending Cliff Hanger for the next two decades, when Picard, assimilated into being Locutus of Borg, issues his threat to Riker "Your resistance is hopeless...Number One." While the typical viewer breathes "Never!" at this, Riker gives the only response it deserves, "Mr. Worf... fire!"
It would have been more awesome had the supposed superweapon not epically failed to work. As TV Tropes points out, even a Curb-Stomp Battle CAN be awesome. The looks on the crew's faces (and the viewer's at home) when the Borg completely No Sell their alleged superweapon was priceless. Keep in mind that everyone watching it at the time was left hanging with that last awesome exchange for an entire summer. It may lose the impact when the cliffhanger's resolved on the next DVD you popped in, but at the time that was pretty much the greatest season finale ever put to screen that didn't involve JR getting shot.
It gets another subtle layer of awesome when you consider this earlier quote from Shelby to Riker: "If you can't make the big decisions, Commander, I suggest you make room for someone who can". Starting from "Mr. Worf, fire", and throughout Part 2, he proves beyond all doubt that he can make the big decisions.
If the superweapon had worked in "Best of Both Worlds", it really would have been an awesome moment for Geordi or Commander Shelby. Riker's awesome moment comes from simply leading one starship into battle against a foe that had destroyed forty starships at once right before that and coming up with a daring plan that works.
Locutus: We will proceed to Earth. And if you attempt to intervene, we will destroy you.
Riker: Then take your best shot, Locutus, because we are about to intervene.
Data gets one when he physically overpowers Locutus, stares him down, and then defeats perhaps the most implacable enemy in Star Trek canon with his mind. Awesome beyond all measure.
Although the character is a subject of much debate, Captain Jellico gets one when he owns the (supposedly secret) Cardassian attack fleet preventing a war before it can start, and gets Picard back in the bargain.
Captain Jellico simply getting Troi to actually wear a freaking uniform would also count — even the spectacular cleavage was getting rather old by that point. Especially for those of us who find her better looking in the uniform.
Data has his day in "Redemption" when he is put in command of a ship with a really insubordinate First Officer. At the critical moment of executing his plan to find a cloaked Romulan convoy, the officer is being difficult and suddenly Data is roaring at him to obey his order or else! It's a moment that took everyone, both character and viewer, off guard to see the android get that tough. Earlier on, the XO comes to Data requesting a transfer. When grilled on why, he admits that he doesn't feel Data would make a good captain because he is an android. Data's response? "I understand your concerns. *beat* Request denied." The look on the guy's face is priceless. What's even cooler is when Data flat out disobeys Picard on a hunch, and turns out to be right! The very same XO who showed him no respect addresses him as "Captain," showing that Data has earned his respect in full. Further building on that, Data comes to Picard, willingly submits himself for disciplinary action for disobeying orders, and gets off with an enthusiastic "Nicely done!" from his CO. And of course, one must remember that Picard was initially reluctant to give Data command of a ship, so Data guilt-tripped him into it.
Gowron's comes at the end of "Redemption" with him triumphant as the new undisputed leader of the Klingon Empire confronting the captured child who dared to claim his position for the traitorous House of Duras. When the child futilely yells, "The Duras family will one day rule the Empire!", Gowron responds "Perhaps," then flashes a wicked grin with those bulging eyes, "but not today." When the other Klingons laugh to Gowron's dark humor, you almost feel compelled to join in.
In "Q Who," Q attempts to join the Enterprise's crew, saying they would need his help against the dangers of the galaxy. Picard snidely refuses, saying they are more than ready for any threat, and so Q hurls them across the galaxy to face the Borg. After failing to heed Q's warnings and losing eighteen members of his crew to the Borg, Riker tries to accuse Q of being responsible for their deaths instead of Picard. Q's only response? (The way that line is delivered is absolutely chilling. With two words, Q proves he's just as dark, dangerous, sinister, and powerful as he is foppish and amusing.)
Q: "Oh, please."
Awesome moment for the Borg, near the end of the episode. Picard has wisely decided to get the hell away from the damaged Borg ship, which starts regenerating itself and tears after the Enterprise in hot pursuit. During the chase, there's this incredible moment where Picard and Riker are watching the Borg ship repair itself after taking a half-dozen torpedoes to the face, and we see this Necro Cam style closeup of the Borg ship knitting itself back together circuit by circuit. The perfect Oh Crap moment.
Three words: "Resistance is futile."
Picard also gets one near the end of the episode when he swallows his pride and delivers one of the greatest Ain't Too Proud to Beg speeches ever:
Picard: You wanted to frighten us. We're frightened. You wanted to show us that we were inadequate. For the moment... I grant that. You wanted me to say I need you? I!NEED YOU!
And Q smirks, snaps his fingers, and sends them all back to Federation space. Point to Picard - the way he delivers it sounds less like being scared into humility than, "This is ridiculous. You want me to beg? Fine. You've thrown us against an unbeatable enemy and eighteen of my crew are dead. I'm begging."
And then there's Q and Picard's final exchange, where Q rightly chides him for the smug sense of superiority that permeated most of the first two seasons.
Q: If you can't take a little bloody nose, maybe you ought to go back home and crawl under your bed. It's not safe out here. It's wondrous, with treasures to satiate desires both subtle and gross. But it's not for the timid.
Best of all? Picard actually learned from this. In an episodic series from a time when character development was mostly forgotten by the end of the episode, for the rest of the series and into the movies, Picard not only lost his sense of superiority, but viewed each new and unexpected situation with a sense of wonder and trepidation. Q basically told him that he was being far too arrogant, and Picard agreed.
Q's moment in "Déjà Q" after being turned human by the Continuum and dumped stark naked on the deck of the Enterprise. No, that's not the awesome bit (though the DVD commentary reveals it was one for John De Lancie). The awesome bit comes later. After a while of getting used to the fact that the crew (especially Guinan) really, really hates him, he can't do anythingwithout his powers, and at least one of the species he's tormented in the past has come back for vengeance, Q is bewildered when Data nearly gets himself killed trying to protect Q from the Callamarain. After a while of trying to absorb this fact, and an "I'm not your father confessor" speech from Picard, Q heads for sickbay and gives a (for once) quiet Data the following speech:
Q: There are creatures in the universe who would consider you the ultimate achievement, android. No feelings, no emotions, no pain... And yet you covet those qualities of humanity. Believe me, you're missing nothing. But if it means anything to you... you're a better human than I.
Q goes off to commit suicide in order to protect a crew that doesn't like him. He totally earned that mariachi band, a very cool Funny Moment.
Guinan mocking the now-human Q, and sticking a fork in him.
Q: What must I do to convince you people [that I'm powerless and mortal]?
Q: Oh, very clever, Worf. Eat any good books lately?
Q seems to get the Butt Monkey treatment by other members of the Q Continuum a fair bit, which leads to a pair of Awesome Moments near the end of the novel Q-in-Law. The first is for Deanna Troi's mother Lwaxana, who goes absolutely nuts when she learns Q's been playing her for a fool in a faux romance. When Q tries to take back the Q powers he'd given her, it fails. An eight-page beating commences, with Lwaxana punching Q into the warp nacelle, using him for a racquetball, and finally turning Q into a tree and nearly chopping him to pieces (starting below the belt) before Deanna and Picard get her calmed down. Her rant after Q's apology only serves to top the whole thing off:
Lwaxana: You're so disdainful of Humanity. Of mortals. You keep saying you're above our emotions, and hold them in such disdain. You know what I think? I think you're not worthy of them. You're not good enough to feel love.
Shortly after that, Q2 shows up and claims an entire second Moment of Awesome when he explains that he was responsible for Lwaxana keeping the powers long enough to teach Q a lesson he'd never forget (complete with taking pictures of Q's beating to show the rest of the Continuum), before hopping over to another spot and hitting Q in the face with the fact Picard was right on target with his Hannibal Lecture: Q is indeed behaving in a very human manner.
Mention needs to be made of the opening scene of "Descent Part I", where Stephen Hawking plays a hologram of himself, and beats Data, Issac Newton and Albert Einstein at poker:
Newton: Blast! I fold.
Data: I fold as well.
Einstein: Ze Uncertainty Principle vill not help you, Stephen. All ze quantum fluctuations in ze universe vill not change ze cards in your hand. I call. You are bluffing, and you vill lose.
Hawking: Wrong again, Albert. (Shows his Four of a Kind)
Which led to a funny and awesome moment in one of the DVD extras where Brent Spiner recounts how some time later he happened to run into Hawking, and the first words out of his, err...computer...were "Where's my money?"
Doctor Crusher gets one in "Descent, part II", when she hides the Enterprise inside a friggin' star to evade a monstrously powerful vessel flown by Ax-Crazy Borg, and then triggers a solar flare to utterly annihilate said Borg ship shortly thereafter. Not only did she take down a Borg ship... she did so with a less than skeleton crew, most of whom weren't even junior officers. And she did so whilst orchestrating the rescue of the crew who were trapped on the other side of said Borg ship. Commander Beverly Crusher is a Bad Ass.
Best part is, as mentioned elsewhere on the page, she's the reason the Enterprise has that metaphasic shielding (which made the star dive possible). She put her career and later her life on the line to prove the technology worked.
And to get specific on those reasons: Troi wakes up as a Romulan and is told she has to give a convincing performance as a Tal Shiar officer or die, against a captain who has a very personal grudge against the Tal Shiar. Troi has no familiarity with the Tal Shiar or Romulan culture beyond what Starfleet knows, but she successfully saves the dissidents from treachery and comes up with a new plan to get them to the Federation by using the Enterprise. Then she seizes command of the Warbird by threatening the families of its crew and contacts the Enterprise without breaking "character" which allows them to beam her out just as the Romulan captain figures it out. And the reason that N'Vek abducts Troi is specifically because of her empathic abilities, which prove to be incredibly useful and shows how competent and useful Deanna Troi's character can be when the writers think about it a little.
Guinan had a Moment of Awesome in The Best of Both Worlds, Part II with her "beyond friends, beyond family" speech to Riker.
Guinan in "Night Terrors", when she breaks up a fight in Ten Forward by blowing a hole in the ceiling with a BFG. (Note: Good thing the ceiling was only an interior bulkhead, and not part of the Enterprise's hull...)
"This is a little souvenir I picked up from Magus III. That was setting number one. Anyone wanna see setting number two?"
The gun's not just for show either. In "Redemption", it's shown that Guinan can shoot better than Worf.
In "Skin of Evil", the Enterprise crew encounters Armus, an alien being who murders Tasha Yar, and attacks Riker, then sadistically gloats about it to Counselor Troi, trapped in a downed shuttlecraft. Throughout the episode, the Enterprise crew tries to reason with Armus, but Picard decides to have one last word with him:
Picard: You say you are true evil? Shall I tell you what true evil is? It is to submit to you. It is when we surrender our freedom, our dignity, instead of defying you.
Armus: I will kill you and those in there.
Picard: But you will still be in this place. Forever, alone, immortal. [Armus begins growling] That's your real fear, never to die. Never again to be united with those who left you here. [Armus is screaming now] I'm not taking you anywhere.
While Armus is distracted by rage, Picard gets Counselor Troi and her shuttlecraft mates beamed onboard, along with himself. He then destroys the crashed shuttle and has Armus' planet declared off-limits, to ensure nobody ever faces Armus again.
Troi gets some pretty solid knocks against Armus as well, knowing that while he says he killed Tasha for his amusement, killing her brought him none of it. Despite the fact that Armus is holding her hostage, one gets the impression that she's the one in control.
The Big Damn Heroes moment by Admiral Riker and the refitted Enterprise in "All Good Things". Beverly Picard's medical ship, the Pasteur, is under attack by two Klingon Birds of Prey, their shields are completely gone, and one more hit would spell doom for our heroes. Then the sensors pick up a Federation ship decloaking. The next thirty seconds are possibly some of the best CG in the entire series, and the coolest aversion of 2-D Spaceever.
The BFG strapped onto Riker's refitted Enterprise. It looks like a phaser cannon, but it blasts a hole clean through an entire Klingon battlecruiser (and its shields), destroying that same battlecruiser in roughly 6 more shots. Then the Enterprise flies through the debris without any concern. Later on, Riker mentions off-handedly that the Enterprise had been due for retirement, and was saved only by him choosing her as his flagship. Makes one wonder what Starfleet's front line ships must be like.
In "Suspicions", Dr. Crusher investigates a Ferengi scientist's murder against orders and at risk of losing her medical license. It ultimately involves her flying the scientist's shuttle into a star to prove that his new shield works, and vaporizing the culprit.
When Dr. Crusher asked Kurak if the lies that Reyga had said to her really were lies?
Kurak: Be careful, Doctor. Insulting the honor of a Klingon can be extremely dangerous.
Beverly: Did Reyga make that mistake?
[a beat, then Kurak throws Beverly across the room and against a wall.]
Kurak: I have heard enough accusations. Now I will have your silence!
Beverly:[gets up, stares at Kurak with equal intensity] Well, you're gonna have to throw me a lot harder than that if you're gonna get it.
In "Allegiance", Picard shows a pair of Sufficiently Advanced Aliens why performing experiments on himself and his crew is a bad idea by trapping them with a forcefield, which causes them to panic, as apparently, they're terrified of confinement. He lets them out, lectures them, and tells them to get off his ship. They do so, utterly cowed.
In "Brothers", Data hijacks the Enterprise, outsmarting the rest of the crew every step of the way having already predicted and blocked their attempts to regain control of the ship before they even try them. Then he calmly walks to the transporter room while multiple security teams can only stand and watch from behind forcefields he'd already laid out in advance.
It is also one for Brent Spiner for playing three very different characters at the same time in several scenes, all of whom requiring plenty of makeup (but especially Doctor Soong) and some really clever filming techniques. So make it one for the special effects team and the editing/filming guys, too.
Riker takes a fair bit of flack, but he scored some points in "The Pegasus", as a result of his speech to the amoral captain he once obeyed without question, as well as his acceptance of whatever consequences were coming to him:
Riker: I wasn't a hero, and neither were you! What you did was wrong. And I was wrong to support you, but I was too young and too stupid to realize it! You were the captain, I was the ensign. I was Just Following Orders.
Then in "Attached", Riker demands the release of Picard and Crusher by firmly pointing out that planet KesPrytt was not Federation material: delivering a "The Reason You Suck" Speech to the lawful-but-paranoid Kes and telling the xenophobic Prytt to expect more unwanted visits if Starfleet doesn't get its officers back.
Wesley teaching all the kids in "When the Bough Breaks" about Passive Resistance, ie, starving themselves so their "adopted" parents would concede and give them back to their actual parents.
In "A Matter of Time", Berlinghoff Rasmussen, a time-traveler from the 22nd century (but using a 26th-century timepod) has spent the entire episode stealing technological devices from the Enterprise with the intention of returning to his time and "inventing" one a year. His ultimate prize is Data, whom he cons into getting into the timepod with him. However, when he tries to stun him with a phaser, he finds that the Enterprise crew has deactivated it.
Data: I assume your hand print will open the door whether you are conscious or not.
Kolrami:Challenge! We do not whine about the inequities of life.
Data winds up playing Kolrami (an insufferable Jerkass) at his favorite game and loses. Data is initially perturbed (in his own way) and wonders if he is defective. When he's convinced he's not, he has a re-match with Kolrami. This time he plays for a draw instead and matches his opponent's every move - forcing Kolrami to concede in frustration. note To put this in full perspective, the game they were playing, Stratagaema, normally ends within 100 moves, due to the rules of the game. Kolrami absolutely stuffs Data in the first match, winning in less than 50 moves. In the second game, when Data doesn't try to win but only fight to a draw, the game goes to just over 35,000 moves before Kolrami gives up. Everyone around comments that they didn't even know the game could GO that long
Data: I busted him up!
Worf's statement to Duras in "Sins of the Father":
Worf: It is a good day to die, Duras. And the day is not yet over.
Worf proves himself a better Klingon than the Klingons by accepting discommendation, the stripping of his family's honors, lands, and titles, rather than let the Empire tear itself apart into civil war.
Picard stood with Worf as his cha'DIch and did whatever he could to help him - even fending off some of Duras' goons while securing a vital witness. When it becomes apparent that the entire trial was a sham and the Empire intends to execute two innocent men, Picard won't back down.
Duras: You have no say in this, cha'DIch! Picard: I speak now as the captain of the USS Enterprise and Lieutenant Worf's commanding officer! You will not execute a member of my crew, nor will I turn his brother over to you! K'mpec: This is not the Federation, Picard. If you defy an order of the High Council, the alliance with the Federation could fall to dust. Picard: The alliance with the Federation is not based on lies, K'mpec. Protect your secrets if you must, but you will not sacrifice these men.
The frail old Klingon woman Kahlest shares one with Picard, who is holding his own in a knife-fight with three Klingon assassins. When Picard is finally overwhelmed, Kahlest ends the fight by hurling a dagger into the last assassin's back from several yards away. Later in the episode, she has this exchange with an old flame who just happens to be the Chancellor of the Klingon Empire:
K'mpec: It is good to see you again.
Kahlest: You are still fat, K'mpec.
Brick Joke: That's the second time she mentioned K'mpec's girth. Just after assisting Picard, she points out that K'mpec tried to court her before..."...but he was too fat."
In the following season's "Reunion", Duras kills K'Ehleyr for looking into why Worf accepted discommendation. Worf ultimately responds by invoking the Rite of Vengeance (a fight to the death), soon driving his bat'leth into Duras' chest.
Duras: (Realizing that he's going to lose) I'm the only one, Worf - the only one who can prove your innocence. Kill me and you're a traitor forever.
There was his entrance to Duras's bridge. Duras is derisive about how Worf is discommodated and not in a position to issue the Rite of Vengeance on a Klingon vessel. Worf steps forward.
Worf: K'Ehleyr was my mate. [Everyone reacts, especially Duras, whose expression is just short of Oh Crap before he demands a sword for the fight.]
In the sadly non-canon novel Strike Zone, we get another example of Pulaski mistreating Data, which ends with a doozy:
Data: Doctor, it's been a very educational conversation.
Pulaski: Why, thank you, Data. I certainly hope you'll be able to store it away somewhere.
Data: And I hope you will as well, Doctor.
Pulaski: Well, Data, not being a machine, I wouldn't know where.
Data: I think, Doctor, you know where you can store it.
Basically anytime Dr. Pulaski is being an asshole and Data stands up to her. This one's from the show proper:
Pulaski: "DAY-ta," "DAH-ta," what's the difference?
Data: One is my name. The other is not.
The episode "Who Watches the Watchers": Just about everything Captain Picard does, absolutely refusing to inflict any religion on the society, rather going directly against the Prime Directive. Moreover, his kind and respectful treatment of Nuria and her people is beyond awesome.
Doctor Crusher in "Remember Me", trapped in an Enterprise where people disappear and no-one else remembers them, keeps her head despite all evidence indicating that she may be losing it. She then works out the truth - that she's inside an imaginary shrinking bubble universe - deduces the universe's origin, locates the exit and escapes. The exit may have been created by her ever-perfect son Wesley (who buggered up the experiment which sent her there in the first place) but only Beverly's rational attitude got her through it.
Roga Danar, the walking Super Soldier of awesome from "The Hunted". He basically spends the entire episode staying one step ahead of the entire Enterprise crew, and kicking multitudes of ass wherever he goes. And he's just one of the numerous genetically enhanced soldiers. The most amazing thing was when the Enterprise crew finally had to transfer him to his native police force's ship. You see the transporter beam take hold, but suddenly, Rogan successfully resists being transported before escaping, before that moment, no Trek character had ever achieved that!
Mention must be made of Worf casually sauntering over to an over loading phaser to turn it off.
Despite the episode centering around Worf, "Ethics" provides these for both Commander Riker and Doctor Crusher (and, arguably, their actors).
Doctor Crusher spends the episode butting heads with Doctor Toby Russell for constantly taking shortcuts, including relieving her of medical duties after a patient dies under her care when she chose to disregard SOP and try an experimental treatment on a patient (according to Russell, the patient would have died either way, this way he at least aided in her research). It culminates in this speech at the end of the episode, delivered with smoldering anger.
Crusher: I am delighted that Worf is going to recover. You gambled, he won. Not all of your patients are so lucky. You scare me, Doctor. You risk your patients' lives and justify it in the name of research. Genuine research takes time. Sometimes a lifetime of painstaking, detailed work in order to get any results. Not for you. You take short cuts. Right through living tissue. You put your research ahead of your patients' lives. And as far as I'm concerned, that's a violation of our most sacred trust. I'm sure your work will be hailed as a stunning breakthrough. Enjoy your laurels, Doctor. I'm not sure I could.
Riker is asked by Worf to give him an honorable death, as he cannot function as a paraplegic. He spends the episode debating if he can do this, then comes to Worf, telling him how little he likes the very idea, considering this to be Worf simply giving up. Then, he says that if it were his place, he would still help him die... But it's not his place. It's Alexander's, his son. But Riker has figured that Worf really can't bring himself to "look at your son and tell him to bring you the knife. Watch you stab it into your heart, then pull the knife from your chest and wipe your blood on his sleeve." So he walks out, leading Worf to decide to risk the treatment that Russell has offered him.
In Time's Arrow, Data is transported to 19th-century Earth. He decides to play poker, and the other gamblers quickly assume he's a chump. One Gilligan Cut later, he took them to the cleaners.
Made better by the fact that he was new to poker in the second season (where he lost badly to Riker) and had spent the rest of the series up to that point slowly improving. And now he beats the professional card sharks at it.
The helm officer, Ensign Rager, had hers by piloting the Enterprise, sideways, out of the Dyson Sphere as the door was closing. And without even scratching the paint.
In "Masks", Picard is able to save the day by Cold Reading a long-dead and unknown civilization, using only his background in archeology.
"Conspiracy" has an Admiral infected with a parasitic species who attempts to get Riker infested. Riker fights back and summons security before being knocked unconscious. The response team is La Forge and Worf who fight back as well, but are also knocked out. Then Doctor Crusher arrives and manages to take the admiral down with a sustained phaser blast.
Fun fact: Every time Doctor Crusher picked up a phaser, she hit her target. Now THAT'S surgical precision.