The northern province of Tamriel is a majestic and sometimes mysterious place. Whether you're looking at the in-game lore or simply enjoying the many quirks and bugs to be that can be found, Skyrim holds quite a few points of interest for gamers besides shouting things off of a mountain.
In regards to quests, there are certain NPCs marked as essential to the function of the game that cannot be killed by normal means. Their life can be "turned off" using console commands, but this doesn't count. Often enough there's valid reasoning for this, but for some reason, there are a few NPCs marked as essential that are not vital at all.
10 Noster Eagle-Eye
Noster is a beggar found in Solitude. He has a couple of minor quests for the Dragonborn, but nothing that most would miss if he somehow died. As a veteran with a vast knowledge of the wild, he can teach the player a thing or two about sneaking around. However, this still does not explain why he has game-given immortality. It is possible that the developers want him to stick around so that the player has a constant reminder of the consequences of war. Although, this is a stretch.
9 Dorian
This newly signed sailor can be found aboard the Red Wave, a ship docked in Solitude's harbor. He can be a target for certain quests like "Hired Muscle," where the player may need to fistfight him, or "Enchanting Pick-Up," where one will need to collect an item from him and deliver it to someone else. There are plenty of other potential targets for these quests, so Dorian's necessity to the game is rather questionable.
8 Gisli
As a noblewoman residing in Solitude, Gisli seems like she is important. Her brother Erikur is a thane in the city, and someone the player can interact with during multiple quests, but his sister does not seem to be crucial in any of them. She has some unique dialogue with the player and her brother but all the information she can give only acts as supplemental information as opposed to important quest-related facts.
7 Amaund Motierre
Amaund can in fact be killed, but only after the quest "Hail Sithis!" He, as a client of the Dark Brotherhood, will offer one of the most important quests in this part of the game. At first, one will think this makes him important enough for the game to label as essential, but given the context of the setting, this seems off.
Everyone making contact with the Dark Brotherhood should be killable right away on the basis that they are knowingly summoning an assassin.
6 Nikulas
Nikulas is a wannabe adventurer in the Skaal Village on Solstheim with dreams of setting out on epic quests. But his mother is not fond of this notion and will ask the Dragonborn to talk some sense into her son. The player can do so for some meager rewards, or they can side with Nikulas and give him a head start on his journey to becoming an adventurer. However, none of this is consequential to the more interesting quests on Solstheim.
5 Jaree-Ra
This Argonian quest-giver can tempt the player into a sneaky venture for some big potential gains but later doublecrosses the player. The end of the quest involves tracking Jaree-Ra down and exacting vengeance in the way of justified murder for his betrayal. However, since he acts quite suspiciously, it would make sense if the player tried to double-cross him before his traitorous act. Trying as much, however, will simply result in Jaree-Ra being downed instead of killed.
4 Rolff Stone-Fist
One of the more openly prejudiced inhabitants of Windhelm, it would make sense for the player to try killing him if his dialog is too irksome. Besides having a scripted conversation that the player can overhear while entering the Stormcloak-controlled city, Rolff doesn't do much.
Well, besides hating on non-Nord citizens of Windhelm and being a potential punching bag for the Dragonborn.
3 Any Commander After The Civil War
During the Civil War quests, commanders on both the Imperial and Stormcloak sides will be classified as essential due to their involvement in various stages of the questline. But after this line has been completed, they still cannot be killed. Even those found in the (now pointless) military camps around the province cannot be permanently dealt with if one engages a camp in a fight.
2 Most Of The Greybeards
Arngeir is an important character and holds a great deal of knowledge that the player can use to their advantage throughout their playthrough. But the other Greybeards don't seem nearly as useful. Besides demonstrating a shout or providing a few lines of dialogue here and there, they don't actually do anything worthwhile. Borri, Einarth, and Wulfgar's roles could easily be filled by Arngeir, so labeling them as important characters in the game's files seems unnecessary.
1 M'aiq The Liar
This recurring character has been a random encounter in the last three main series Elder Scrolls games. In Skyrim, he can be found wandering the wilds on adventures and will always supply a few bits of unique dialogue depending on the surroundings. He is even one of the few characters that will not be afraid of the Dragonborn if they approach as a werewolf or vampire. Despite his many unique qualities and interesting anecdotes about the game (with some that even break the fourth wall), M'aiq is not required for any quests. His existence is solely to provide his charming and funny thoughts on the land of the north. As to why would anyone want to harm this loquacious wanderer anyway we cannot say, but his essential tag is a bit suspicious to say the least.