I think I've Seen It a Million Times, but can only recall a few specific examples. Power is sweet, but that pesky "mortality" thing makes it so transient. What if you can get rid of it? After all, if you rule a country, you've got all of its resources at your fingertips to sponsor a research into an immortality serum! Nowadays it's considered not kosher for political leaders to have too long terms, even if they are completely humanly possible, so this character can easily be presented as an amoral tyrant. But in settings with no democrats around, they can be alternatively presented as a good, responsible ruler who wants to preserve an age of prosperity in their country. Of course, if the immortal ruler is undead or employs some kind of blatant Immortality Immorality, all arguments are moot: this is, most definitely, a villain, quite possibly a Big Bad. Note that this is different from a Society of Immortals which logically has to have an immortal leader, too. The ruler has to have mortal subjects to qualify as this trope. A subtrope is God Emperor, when the ruler has some more extraordinary perks along with immortality (if they aren't simply delusional, of course).
- His Divine Shadow from Lexx, who resorted to the body-surfing kind of immortality.
- Transhuman Space gives us the Kazakhstani dictator Zarubayev, who hogs all transhumanist tech available in his country to cling to life indefinitely.
- The Civilization series of games is this trope meeting Gameplay and Story Segregation: in terms of gameplay, every civilization is stuck with one leader for the entirety of human history.
- The Tribunal from Morrowind are of the morally ambiguous variety; it's true that one of them went totally bananas and became a Big Bad of TES 3: Tribunal, but they also did a lot of good to the Dunmer race.
- Also from this 'verse, many Telvanni magelords use necromancy to cling to life much longer than Muggle elves can. One of them, Divayth Fyr, is of the same age as the Tribunal (and he's a nice guy running a hospice).
- The Nazgul from Lord of the Rings started as this, until they got completely degenerated into evil servitor spirits with little personality of their own.
- The Undying Court from Eberron are undead elves who are the de-facto rulers of the Elves of Aerenal. Also King Kaius of Karnath is over 125 years old due to his being a Vampire, but his subjects don't know it due him pulling a My Grandson Myself. His rule was not continuous either.
- In many Dungeons & Dragons settings, Githyankies are ruled over by a Queen who is a Lich, named Vlaakith. There's been multiple Vlaakith, many of them Liches who ruled for centuries before being replaced by another who takes the same name (Though some settings and books imply there's ever just been the one). The current is Vlaakith CLVII, who never had an offspring before dying and becoming a Lich, as such she has ruled for over a thousand years (Her mom ruled as a Lich for 600 before being destroyed).
- In Mistborn, the Lord Ruler has been in charge for a thousand years. The results have not been pretty.
- Golden Sun: Babi has been ruling the city of Tolbi for far longer than any human could thanks to a magical life-extending draught he stole from Lemuria. He tasks the heroesof the first game to get him some more. In the second game, we're brutally informed that he's dead, and the whole matter is dropped.
- A smaller scale example from Discworld: Mr. Slant (a zombie) and an unnamed vampire are the heads of a law firm, and intend to do so for quite some time (a clerk there remarks that dead men's shoes are currently filled by dead men).
- In the Iron Druid Chronicles the immortal druid Atticus played this role for a few centuries. Fleeing Europe, he joined an African tribe and after a while became its leader. He married and shared his rejuvenation potion with his wife and children. The tribe prospered and his immortal family became the ruling elite of the nation that formed. However, after his wife was killed, he became disillusioned by how decadent and immoral his children became as a result of their immortality and left them and the country to fend for themselves.
- Grand Maester Mika from Final Fantasy X has been the leader of the Church of Yevon and the de facto ruler of Spira for a very long time. It is revealed that he is in fact an unsent, a deceased ghost who remains tied to the mortal world.
- Obligatory My Little Pony: Friendship Is Magic example: Princess Celestia is immortal and has ruled over Equestria for at least 1,000 years, if not much longer.
- Buffy the Vampire Slayer: The Mayor of Sunnydale has been mayor for over 100 years. He founded the town over the Hellmouth so he could ascend into demonhood, coincidentally on Buffy's graduation day.
- In the Doctor Who serial "State of Decay" the Three Who Rule are the captain and his Executive Officers from a ship that crash landed on the planet long ago. The peasants have gone through many generations but the Three are still the same people, because they're vampires.
- Emperor Scientist Solomon Petresun in the Starsiege series lived and ruled Earth for at least several centuries via technological immortality he invented.
- Needs More Examples!
Hello, Unknown Troper. You'll need to get known to lend a hand here.