Based on your question, you might dig the book “Boat of a Million Years.” The author put quite a bit of thought into just that.

https://en.m.wikipedia.org/wiki/The_Boat_of_a_Million_Years

Science fiction is going to age poorly. A lot of it is already hilariously dated. Look at most of Star Trek. They're flying at FTL speeds through space with artificial gravity, teleportation, lifelike androids, and replicator technology, but their screens absolutely suck. More and more of those inconsistencies are going to add up over the centuries and make things ridiculous after a while.

The number of new things that people enjoy dwindles with age. Just about everyone agrees that the music that was being made when they were teenagers is the epitome of the art. Are you going to be able to enjoy anything when you're 2563 years old?

The older you get, the faster time apparently moves. Having grown up in the 80s and 90s, on some days, even "The year 2000!!" still feels like it should be the future to me. I can't imagine what even a few centuries would do to this phenomenon, let alone a millennium or megaannum (I had to look that word up.)

On the upside, presuming I'm the only immortal, I'll be the only person currently alive to see if they actually finish that performance of Organ^2^/ASLSP in Halberstadt.

Friends, family, and lovers dying before you.

Either "Boredom: After some time you have seen basically everything." or "Can't keep up: The world changes so fast, and I'm, stuck in a mindset I acquired in 1543".

And: Bureaucratic nightmare. "We have you on file as being born in 1924, but you don't really look like a centennial. Can I see your passport instead of that of your great-grandfather, please?"

Getting imprisoned for thousands of years unable to get out.

Wage slaving never stops

If other people are also immortal, the awkwardness of all of them eventually becoming your exes

On one hand, you have eternity to come to grips with everything you've done. On the other hand, it might take eternity to come to grips with everything you've done.

Seeing all of your friends and family die, knowing you'll never stop missing them.

Having the perspective of centuries. Seeing society make the same mistakes over and over again because they forget, but you never do. It would drive me mad. Already does, considering I have the ability to, and have, read history. I just imagine living it over and over to be tedious.

The disappointment of experience winning lifetime supply of something but that would eventually turn into a lie

Having potentially thousands of years of embarassing moments of social awkwardness to think about. And, over the aeons, being relieved when the people you know and love die because they won't remember the things you're so ashamed of.

Btw if you were actually immortal, after a while you would just go into shock and enter a vegetative state from all the psychological stress.

Having to listen to that Queen song, forever.

You'll be perpetually behind the times. People tend to get set in their ways even by their 30s. You'll constantly lag behind the trends, language, and tastes of the younger generation...

If you were the first to be immortal, you may not have the best version of immortality and it may render you incompatible with better, future types of immortality. Like magical regeneration that prevents you from getting a personality upload to a cyberbrain that is a million times faster and smarter than the squishy biological brain.

Being eaten by sea anemones, tuna, sharks, swordfish, sea turtles, penguins, and other jellyfish.

https://en.wikipedia.org/wiki/Turritopsis_dohrnii#Predation

I don’t think you’d remember a break up from hundreds of years ago, let alone be upset about it.

Either humanity gradually grows to despise you for your ancient morals

or they don't ever meaningfully surpass where we're at today.

Everyone else in your life that isn't immoral (if you're the only one who is) dies eventually, so every time you make a friend or start a family, you do so knowing that you will have to watch them all die someday.

Not being able to kill yourself.

One of my books features an immortal protagonist and I've as such thought about this quite a bit. More than the answers already provided here, what I found interesting as a writer was the balance I needed to find between making an immortal detached from mortal values while still being engaging to mortal readers.

Said as a pithy question, if you can outlive everyone's decisions and mistakes, what would it take to make you do anything at all?

Idk id be super depressed if I was able to experience my family, friends, family's children, and so on die.

Loneliness. I think being immortal would show someone what true Loneliness is

I think you're undervaluing loneliness. Loneliness isn't just missing some one. Loneliness means there's no point in connecting with people because they will just die. Loneliness means that no one knows the depth of your condition because it isn't available to them. It means that as they change and face new obstacles, you'll be oblivious to all of that. You'll not only see them die, you'll see the vitality deep out of their pores as they age. All the while you'll never know what that means personally or feel that slow slipping.

Also, super weird that your example is a breakup and people dying is something not worth registering.

LoL investing and compounding! I literally have all the time in the world.

I suppose it depends on the rules of this specfic immortality. As someone who lives with chronic pain that literally never feels physically comfortable in any position, immortality sounds like a cruel joke. Not that I'm suicidal or eager to die, but the fact that it would progressively get worse and worse without any sort of end is.... horrorific.