The series premiere ends with a battle between the two Alpha Quadrant ships and Kazon. While Voyager acquits itself well, the Maquis ship is barely able to hang on much less help Voyager. However, in order to take some of the pressure off Voyager's back, Chakotay weaponizes his ship by using it to ram the main Kazon ship, destroying the vessel and giving Voyager the edge it needs.
Janeway's Badass Boast to Maj Cullah when he tells her that if she takes the remains a replicator the Kazon built from Voyager's technology, she'll be committing an act of war.
Janeway: You know, I'm really easy to get along with most of the time, but I don't like bullies and I don't like threats, and I don't like you, Culluh. You can try and stop us from getting to the truth but I promise you that if you do I will respond with all the 'unique technologies' at my command.
In "Basics, Part 2," Tom Paris destroys a Kazon ship while in the middle of fixing his own damaged shuttlecraft. Actually, what happens is, a fed-up Paris yells "I don't have time for this!!", comes to a complete stop, lets the Kazon ship naturally get ahead of him, and then blasts them into oblivion just for pissing him off. Repeat: he took down a Kazon ship with just a shuttlecraft. And then he goes on to retake Voyager from the Kazons with the help of the Doctor and Suder.
Speaking of which, Lon Suder infiltrating Engineering, single-handedly taking out 11 Kazon (without missing!), and overloaded a backup phaser coil, killing Seska - and, tragically, himself - and allowing Tom Paris to retake the ship. After all his desperation in part 1 of wanting to contribute something to the ship as atonement for his crimes, it makes this sequence all the more powerful as he does just that - and itkills him.
Chakotay saving a native woman from an erupting volcano was seriously Badass.
Tuvok had a really good one in "Prey". A member of Species 8472 has infiltrated a part of the ship and depressurized it. The crew members have split off in pairs to try to hunt it down, with Tuvok and Seven as one of the pairs. As they walk down a darkened, gravity-less hallway, they turn a corner and Seven spins and fires at something in the air. The camera pans and we see a floating datapad hanging in midair, spinning gently. It pans back to the two of them and Tuvok looks at the datapad critically, turns to Seven and calmly declares, "You missed."
Janeway had one where she and holo-Leonardo da Vinci built one of his Renaissance-era gliders, and used it in an escape plan. Thoroughly cool.
"Dreadnought" is forty-two minutes of CMOA for B'Elanna, especially when you consider that she was the one who programmed Dreadnought, so its frequent CMOAs in the episode also belong to her by proxy. Too bad she doesn't really get another set of CMOAs at this level until "Juggernaut."
"The Thaw" is a particularly cherished moment of awesome by Janeway fans. Several people are stuck hooked up to a virtual reality that is being run by a personification of the emotion of fear, who can only exist as long as there are terrified people connected to the system. Janeway manages to convince it into a "hostage exchange" where she takes the place of everyone else it's got in the simulation, then once everyone else is safely free, she reveals that she tricked Fear with a computer-generated Janeway, and isn't really connected. As Fear begins to fade away into nonexistence he whimpers "I'm afraid," to which Janeway responds with a cold "I know." See it here: 
From the same episode, the Doctor's handling in his first encounter with the Clown.
The Clown: How am I supposed to negotiate if I don't know what your thinking?
Doctor: (stone faced) I have a very trustworthy face.
Even the Doctor's first appearance is awesome. The fear clown and his entourage is getting more and more rowdy, strapping Harry to a table and just as he's about to slice into Harry, the Doctor casually takes the clown's hand from out of frame and calmly admonishes him for his incorrect handling of a scalpel.
Kes had her big moment facing off with a powerful telepath. With the alien having incapacitated the entire rest of the ship with various illusions, she manages to look him in the eye and turn his power against him, halting the illusion and hitting him with everything he just subjected her to. By the look of it, he wasn't quite so prepared to take it...
The alien gets one a moment later. He's lying on the floor in pain, and Janeway starts asking him about exactly how he creates the illusions (so they can stop him from doing it in the future) with a look that suggests she's just barely holding back the urge to kick him while he's down. He looks up and says:
Botha: "I'd really like to accommodate you, but you see...I'm not really here." (*vanishes*)
In the episode "Blood Fever", B'Elanna takes one of the boldest steps of female empowerment shown in any Star Trek series by naming herself as her champion against Vorik. And by the way he treated her in his pon farr, particularly since he ended up infecting her with it, he definitely had it coming.
Seven had several as well, but to cite one in particular, a Hirogen demands that she sing (her persona in the holoprogram having been a lounge singer). She refuses even as the Hirogen pulls a weapon on her and Tuvok attempts to convince her that getting herself killed over this isn't logical.
For the Doctor, pick a moment from "Tinker Tenor Doctor Spy," especially the pre-credit sequence and the transformation into the ECH.
Toward the end, as acting captain, he manages to bluff the aliens with a fake weapon in either a rip-off or homage to the episodes "The Emissary" from DS9 and "The Corbomite Maneuver" from TOS respectively, depending on who you ask. And he does it with style.
Doc: Tuvok! Activate the Photonic Cannon! (beat) Tuvok, that was an order!
Tuvok: Activating the Photonic Cannon... Sir.
When the Doctor actually got to be the ECH in "Workforce", he didn't let it go to waste. When informed by some scavengers that they intended to seize his ship, he opened fire on them without a second thought and they were disabled in moments.
Kes had another moment when she'd been body-snatched by an evil warlord. First, when you saw what the warlord did with Kes's powers... well, you learn why a Badass and very maleBig Bad would want to spend the rest of the foreseeable future in the body of a waifish girl. (Of course, he didn't know that as an Ocampa, Kes, if she takes very good care of herself, will live to the ripe old age of nine, at best.) Then you find out the body's true owner's not as weak as the villain thought. He starts being driven mad, saying things that sound more Kes-ish than evil warlord-ish, and then we get a Journey to the Center of the Mind in which he confronts Kes. Tieran gives his speech of evilness, and Kes lets him know that he's messed with the wrong "little girl," ending with:
Kes: "I won't stop until you're broken and helpless. There's nowhere you can go to get away from me. I'll be relentless, and merciless, just. Like. You."
At which point, Tieran awakens, and it turns out that he's actually been out for much longer than the few minutes that he experienced. And he is terrified. Of course, quoting it doesn't give you the full effect, which takes Kes' badass delivery. That's right, "Kes' badass delivery."
Another one for Janeway: after the ship is split into two equal versions and Vidiians invade one of them, that ship's Janeway destroys the ship to save the other one. When the Vidiians enter the bridge, Janeway flashes them a big smile and says "Hello. I'm Captain Kathryn Janeway. Welcome to the bridge." BOOM!
Although Voyager was notorious for its love affair with the Reset Button, it managed to push it in high style in the episode "The Year of Hell." In simple words: "Time's. Up.". More specifically, Janeway hit the Reset Button with VOYAGER ITSELF.
Also when she flew through that binary cluster to scare the aliens off the ship in "Scientific Method".
The whole last half of "Pathfinder" is one for Barclay. After his radical procedure to contact Voyager is turned down, he breaks into the lab after hours to do it himself. After he's found out, he quickly transfers the controls to a holodeck simulation of Voyager and continues to run through the procedure, all while evading the guards chasing him using various tricks he's learned from his extensive time spent in the program. Finally, when he's caught and forced to give up, thinking his plan was a failure, a message comes through from Voyager and he's completely exonerated.
When Voyager discovers con artists have been impersonating them, Tuvok faces his double in an underground corridor:
Fake Tuvok: Logic would dictate that neither of us has the advantage.
Tuvok: Your logic is flawed.
He proceeds to shine a flashlight in the fake Tuvok's eyes before stunning him.
The climax of "Shattered" is one for the entire crew. The ship is split into different time frames, and the final console needed to fix everything is in engineering, currently populated by Seska and the Kazon. To fight them, all the crew members from the various time frames join forces: Chakotay from the present day, Janeway and Kim from before the ship leaves the Alpha Quadrant, an adult Naomi and Icheb from the future, and B'Elanna who is still in the Maquis, and a version of Paris most likely from a slightly alternate present. The coup de grace comes when Seska takes Janeway hostage but is stopped by the last arrival: the fully Borg Seven of Nine.
Then there's the way Janeway gets Magnificent Bastard Chaotica to inject one of the packs for her — seconds after he was ready to kill her.
The Doctor's rescue of B'Elanna and Chakotay in "Future's End, Part 2". "Divine intervention is... unlikely," indeed.
Ensign Harry Kim, "Timeless." Unfortunately, it's pretty much the only episode for the Ensign to shine.
Harry still has his moments in some episodes (though many didn't revolve around him). Such as saving baby Naomi Wildman from the duplicate Voyager in "Deadlock," before the ship explodes.
Hell even in one of his earliest focus episodes, "Emanations," Harry has the sheer brass balls to seal himself up inside a death chamber, literally killing himself on the gamble that Voyager will find and revive him in time.
Not once but twice, Harry Kim was the brains behind an explosive device that tricked enemies. First, in "Dark Frontier," when he designed a torpedo to be beamed to a Borg vessel, and destroy it. Second, in "Workforce," when he made attacking aliens think that the crew was abandoning ship, filling the escape pods with bombs!
Kim also outwits the Hirogen, who have taken control of the ship and mind-controlled the rest of the crew, in "The Killing Game." Even better, it's a great Let's Get Dangerous moment — the Ops officer, aka the guy whose job basically touches every system on the ship, is ideally suited for acts of secret sabotage.
And yet, after all that...he still never gets promoted, and the fans still call him "the dweeb."
When alien invaders were switching out the crew for themselves one by one, a couple of extras and Chakotay were the only ones left on the bridge and got to kick major ass before being neutralized.
And of course the whole "lower decks"-themed episode where Tuvok takes four surly crewmembers and over the course of one episode, turns them into kick ass machines of awesome. When they save Tuvok against orders...
Tuvok infiltrating a black market for violent emotions on a world of disciplined telepaths, and managing to get their interest and disable them by telepathically revealing WHY Vulcans prefer to repress their emotions.
Earlier in the same episode, Ensign Kim is being psychologically tortured by the Fear avatar, who is about to start on physical torture by slicing Kim open with a scalpel. Cue, from offscreen:
The Doctor You're holding that wrong.
He proceeds to grab the scalpel and demonstrate the correct grip, saving Kim.
"Counterpoint" is a CMoA for the writers in general, but the best part is Janeway giving The Reveal in her best calm "don't you wish you'd figured it out" voice:
The Doctor escaping Voyager in "Renaissance Man", which finishes with him, disguised as a pregnant Torres, beating Tuvok in hand-to-hand combat by flipping off of walls. Parkour was never so justified in Star Trek.
Borg: We are the Borg. Existence as you know it is over. We will add your biological and technological distinctiveness to our own. Resistance is fu... (both Borg vessels are instantly blown to bits)
Janeway going after the macroscopic macroviruses in season 3's "Macrocosm." That is, after Neelix gets Worf'd, and Janeway responds with a kickass Lock and Load Montage.
After a mind-meld with a murderer, Tuvok loses control of his emotions and finally shows us why Vulcans maintain such tight emotional control: he becomes manipulative, downright brutal in attacking peoples mental/emotional weak-points, and even attempts to use his telepathic powers to control Kes before demonstrating how strong a Vulcan is by trying to shove his hand through a forcefield!
The fact that Janeway, in Scorpion, had the guts to form an alliance with the Borg and keep them from assimilating everyone on the ship, collaborate with them to take down Species 8472, completely shut down Chakotay as he's arguing that it would be so much safer to just give up and appears to send him to the brig. Then when Seven of Nine tries to backstab them as expected, she has a perfect back-stabbing of her own up her sleeve which utilizes the very commander she recently shouted down. In the end, Voyager strolls away having out-backstabbed the Borg, defeated Species 8472, and gained a drone and through her tons of new Borg technology.
Scorpion has Music of Awesome. The score seems to evoke the TOS era danger music and TNG's The Best Of Both Worlds.
Whenever things get dangerous, Voyager's crew tosses aside the little phasers and pull out the big guns.
Seven of Nine may be a Ms. Fanservice, but she has a few of her own. A small one comes when Tom tries to make her join his Captain Proton holoprogram. Instead of putting up with the complete overdose of cheese, Seven walks up to the oh-so-intimidating robot, says "I am Borg," opens a panel and pulls out a cord. She then turns to Tom and asks if she may leave now.
Pretty much everything the Doctor does in "Critical Care," when he finds himself trapped in a morally bankrupt hospital and in just a few days figures out how to manipulate the system so that all the patients get the treatment they need.
At the end of "The Fight." When Chakotay is delusional, sleep-deprived, and running a fever, he can still function well enough to bring Voyager out of Chaotic Space.
...and while we certainly can't list them all (with Chakotay being one of the more battle-oriented characters), this one needs a mention: in "The Haunting of Deck Twelve," when B'Elanna exclaims that she can't shut off a forcefield, and Chakotay calmly takes out is phaser and shoots it, solving the problem.
I submit... Admiral Kathryn Janeway. Crowning Admiral Of Awesome.
Voyager showing off its future tech. Not since Species 8472 has one ship been so awesome.
Future!Janeway: Must be something you assimilated.
Not to mention:
Future!Janeway: Just enough... to bring chaos to order.
The big Kes moments are mentioned above, but Kes has a more subtle one. The Doctor has programmed himself with a 29-hour Levodian flu to mimic the symptoms of being sick, saying that it's an attempt to show the crew that they overreact to medical matters and that they should not be "coddled." Then he begins to panic when the 29 hour flu has gone on for thirty hours. It turns out that Kes tweaked the program a little.
Kes: Knowing when it would end didn't exactly make it a fair test, did it, Doctor?
The Hirogen "Commandant" deconstructing Nazi ideals and harassing a holo-Nazi about it in The Killing Game.
Rise features normally nice guy Neelix finally getting tired of Tuvok's verbal abuse and tears into him. From this point on, Tuvok softened a bit on Neelix although Neelix pulling a heroic moment at the end and saving Tuvok's life helped.
The entirety of Flashback from the very second we see Sulu step into frame until the very end.
In "Resolutions," the crew — having controversially abandoned a disease-ridden Janeway and Chakotay — has several. First, there's Harry freaking Kim spearheading a near-mutiny and devising an ultimately successful plan to bargain with the Vidiians for a cure. Then there's Kes talking Tuvok into relenting. Then there's Tuvok himself, demonstrating his credibility as Voyager's tactical officer by giving Kim's initial plan the improvements it needs to be successful — as well as his command during the battle itself, which ends up being a pretty awesome Misfit Mobilization Moment for Voyager's crew.
Captain Janeway basically telling DEATH to go fuck itself in "Coda." Kate Mulgrew's delivery is epic.
"Go back to HELL... coward!"
Icheb's big moment comes in "Imperfection," when Seven's cortical node starts shutting down, endangering her life. After it's determined that harvesting a node from a dead drone won't save her, Icheb comes up with a way to not only donate his node to her, but also adapt himself to survive without it. And then, when Seven refuses to let him risk his life for her, he forces the issue by disconnecting the node himself while giving a speech about helping others that makes Seven, Janeway, and the Doctor acknowledge that he's no longer Just a Kid.
When Admiral Janeway starts revealing the future to her younger Captain-self, who is uninterested for the most part for fear of violating the Temporal Prime Directive, until that is, she hears about Tuvok's inevitable fall from sanity:
Captain Janeway:"What about Tuvok?"
Admiral Janeway:"You're forgetting the Temporal Prime Directive, Captain——"
Captain Janeway: "TO HELL WITH IT!"
Voyager equipping its armor from the future and transphasic torpedoes. For the Borg, resistance is futile.