Kryten's debut episode. The kind but obsessed neat-freak robot is found still tending to a crew that has been dead for three million years because he has no other purpose. Rimmer immediately puts him to task performing endless menial tasks. Lister tries to get him to stop acting like a slave and think for himself, but to no avail. At the end, he is painting a portrait of Rimmer while he gloats to Lister... whereupon Kryten reveals that he has been painting a portrait of Rimmer on a toilet. Kryten proceeds to insult Rimmer, flip him off and leave on Lister's space bike.
His speech to the title character in "The Inquisitor", which can basically be summed up as "Yeah, I'm a waste of space, but look what I had to work with." It works.
In "Out of Time":
Rimmer: Have we got any chance of winning? Kryten: Their craft is greatly upgraded. We have no chance whatsoever. Rimmer: ...Then I sayfight. Kryten: ...Mr Rimmer? Rimmer: Better dead than smeg!
And Rimmer being the only person left, and deciding to be heroic and attempting to destroy the time drive. It's ambiguous if he does or not before their Starbug is blown up, but they survive anyway.
Deciding to become the new Ace Rimmer in "Stoke Me a Clipper". With the completely awesome reveal that enough Rimmers have become Ace for a time that in one dimension there is a Saturn-like planet with rings made up entirely of their remains.
Rimmer: Not today, matey! (Groin Attack) Remember, only the good die young! (runs) Death: That's...never happened before.
Followed by the credits:
THE SMEG IT IS!
Also doubles as a nice Call Back to his and Lister's conversation in "Future Echoes", about trying to cheat death by beating up the Grim Reaper when he comes to collect your soul.
'He's Arnold, Arnold, Arnold Rimmer, more reliable than a garden strimmer...'
In The Last Human, Rimmer goes toe to toe with the Big Bad in a PAINT STRIPPER and lives up to the expectations of his illegitimate son, a rough and tumble space marine which frees him from his many neuroses and allows him to become a hero of Ace Rimmer proportions... and is then shot in the light bee. Somehow he survives and performs a Heroic Sacrifice to defeat The Rage and allow his friends to reach shelter. The ending implies that this act allows Lister and Kochanski to rebuild the human race.
In Back to Earth, when he kills Katerina by pushing her in front of a car, just after she explains why killing holograms is okay to justify her killing him. Complete subversion when you consider that he's usually the one whose attempts to quote weird regulations are thwarted by someone more knowledgeable.
Even better when you realise it's a Call Back to the Series III episode The Last Day where Rimmer remarks on how most people don't get time to realise a bus is about to kill them.
Well at least he gets 24 hours notice! That's more than most of us get. All most of us get is 'Mind that bus' 'what bus?' splat.
Not just Rimmer, but, every character's confrontation with the Inquisitor.
Here's the Cat (successfully) justifying his existence to the Inquisitor:
Cat: I have given pleasure to the world because I have such a beautiful ass. Inquisitor: Some might say that's a pretty shallow argument. Cat: Some might say I'm a pretty shallow guy. But a shallow guy with a great ass!
Here's Kryten's, which unfortunately doesn't work, though it sure is awesome to watch him shake the Inquisitor's resolve, even if it was just for a moment:
Inquisitor: Well Kryten, justify yourself. Kryten: I'm not sure I can. Inquisitor: But surely your life is replete with good works. There can be few individuals who have lived a more selfless life. Kryten: But I am programmed to live unselfishly. And therefore, any good works I do come not out of fine motives but as a result of a series of binary commands I am compelled to obey. Inquisitor: Well then, how can any mechanical justify himself? Kryten: Perhaps only if he attempted to break his programming and conduct his life according to a set of values he arrived at independently. Inquisitor: Your argument invites deletion. Kryten: The rules are yours, not mine. Inquisitor: Do you wish to be erased? Kryten: Well, I am programmed not to wish for anything. I serve. Inquisitor: In a human, this behavior might be considered stubb-orn. Kryten: But I am not human, and neither are you. And it is not our place to judge them. I wonder why you do? Inquisitor: Enough.
And Lister's minimalist reponse:
Inquisitor: You've got brains, man, brains you never used. Lister: Spin on it.
Lister's final confrontation with the Inquisitor, where he defeats him by outsmarting him. Using his own time gauntlet against him, he manages to erase the Inquisitor (and all his work) from history. To be fair, given that the Inquisitor is a Nigh InvulnerableImplacable Man with a massive Healing Factor that can shrug off an attack from a laserchainsaw, this is likely the only thing that would have worked.
In the opening sequence of "Stoke Me a Clipper", Ace Rimmer escapes a death trap, surfs a crocodile from a plane while shooting Nazis, gets shot and only complains because "This was my best top, dammit!", saves the Distressed Damsel, escapes on a motorbike while shooting more Nazis and has sex with said Distressed Damsel before seeking first aid. What a guy.
Normal Rimmer did a surprisingly good job at fending off the holo-knight, even if it was just Lister in disguise.
Cat rarely shows how much of a Bad Ass he can be. But one can't deny he did some fancy foot work in evading those two bazookoid shots in the first "Polymorph" episode.
"You either got it or you ain't. And boys, you ain't even close."
"White Hole", where Lister plays interplanetary pool (that is pool with planets) and successfully pulls off a trick shot.
The end of "Gunmen of the Apocalypse". The crew finally reach the cockpit moments before crashing into a lava moon. Desperate attempts to pull away lead to them crashing into the lava. A few moments pass..."YEE HAAAAAW!" They emerge again, and fly away (segueing into to a special Western version of the Theme Song, at that).
"Gunmen" gets a few of these. The bit where Lister defends the drunken Sheriff Kryten using Brett Riverboat's knife skills (particularly the apple) and "The Riviera Kid"'s trick shot to prevent Kryten from escaping town both spring to mind.
From "Queeg", Holly teaching the others a lesson about appreciating him more by making them think he's been replaced with a by-the-bookdrill sergeant of a computer AI who makes them work for every bit of food.
Holly: We are talking jape of the decade. We are talking April, May, June, July and August Fool [...] The moral of the story is, appreciate what you've got because, basically, I'm fantastic.
"Emohawk: Polymorph II": Ace Rimmer and Duane Dibleyin the same episode. Especially when Ace decides to jump on the activated grenade, not even knowing that he would be completely safe.
Kryten again, in "Beyond a Joke" when the rest of the crew prioritise a VR version of Pride and Prejudice over Kryten's elaborate anniversary meal. After attempting to assassinate the game characters with mixed success, he imports a tank from a World War 2 game. 'Supper... is... ready!' BOOM! (And yes, that is the tank that James Bond drove in Goldeneye.)
Lister's scene in "Holoship", where one of the genius holograms scouts Starbug. After being insulted, Lister proceeds to start mocking the guy and then threatens him for being a stuck up jackass. When the hologram reminds him he can't be hurt, Lister mentions they have a holowhip, and starts looking more and more deranged, eventually eating his cigarette as he squares up. The hologram flees. (The cigarette part wasn't scripted. To this day, actor Craig Charles admits he has no idea as to why he ate the cigarette.)
In the Series X episode "Fathers and Suns", Lister drunkenly records a message to offer himself some fatherly advice, which consists of chewing himself out for not making something of his life and forcing himself to take the course on Robotics. Later episodes show that Lister is indeed studying for this course, showing that his tough love approach and advice did stick.