Most of these posts reminded me of things I thought were real funny, and in-so-doing reminds me of how much I enjoyed them; thus, repeating the cycle and qualifying them, in my mind, as 'never getting old' events...
Relating to finishing moves:
Going through three consecutive finishing moves when playing on legendary with firebolt or similar spell or with low damage weapon.
Thinking to myself, "Yeah! You can do it!" or "Oh! Maybe! Maybe this time you'll kill 'em!"
Flames or Frostbite spells locking you into a finishing move while the animal/creature, usually a mudcrab, elk, wolf, or fox unashamedly continues to encroach, look at you in surprise, nip at you, or run away; apparently oblivious to your existence, respectively.
Finishing moves where the victim flies off having been delayed by the cut-scene animation.
Relating to scripted lines in general:
Being killed and then scrutinized for leaving "litter" lying about.
An aggressor blocks your attack, or other similar instance where the act of fighting is seen as somehow trivial, and says, "Weren't expecting that, were you?"
The moment when Nurelion is exposed to the fact his Phial has been restored. He will make any number of death gasps and flail out upon dying. Yes, I have a save file of this. I watch it daily. Similarly, the dying mage out front Mzulft does this too, however, it isn't anywhere near as funny.
The older woman in the Dawnstar Sactuary. "You can let me go now. It'll be our little secret."
Misc:
Completing Malacath's quest to acquire Volendrung. Also, I always get a kick out of when it is announced: The new leader, and afterwards everyone is perplexed as to Malacath's reasoning.
When a target dies paralyzed.
When a target dies paralyzed and then gimps out and flies around the room/area.
Casting Calm, Pacify or Harmony, especially in scenarios where it was not expected or "programmed", i.e. Calming Estormo will calm him, but he doesn't drop his hands.
When two Orc Hunters spawn next to eachother, they'll both simultaneously utter intimidations and threats to warn the other off. Since neither will back down (because both spawned there), this results in a battle Orc vs. Orc. This is another I have a save of because it is both funny and entertaining. So far the Orc on the left has a better K/D; watched daily.
Noticing hanging moss in places I hadn't before.
Musicians playing without their instrument.
Whenever Giants stomp and threaten rabbits or other "small" animals... Like, seriously... Chill out!
There are probably others that truly don't get old, but I can't think of them now.