Apocalypse is often referred to as the first mutant, and while the veracity of this boast varies from adaptation to adaptation, he's pretty much the same age across the board - 5,000 years, give or take a few centuries. He's also a mainstay of various dystopian futures. Apocalypse does however, change bodies, so it's not quite the same age in every body.
Exodus and Mr. Sinister were both granted extended/immortal lifespans by Apocalypse, in the 12th and 19th centuries respectively. Interestingly, they both ended up turning on Apocalypse, though for very differentreasons.
Mystique, Destiny, Sabretooth, and Wolverine are (or were, in Destiny's case) "young" immortals who are no more than 150 years old apiece. Of the four, Sabretooth is probably the oldest, being mentioned by John Byrne and Chris Claremont as being fifty years older than Wolverine who was born in the late 1800s. Destiny isn't far behind, as she is in Marvel continuity the historical Irene Adler of the Sherlock Holmes stories, which places her birth as somewhere in the mid 1800s. Wolverine is younger than those two, as previously mentioned, but not by much. And fitting her codename, Mystique's actual date of birth is completely unknown, but it is known that she was young when she met and began working with Destiny, so she's probably around the same age.
There's also Belasco, who was born in 13th century Florence and met Dante.
Selene's lackey Eli Bard and the Incredible Hulk villain Tyrannus (who the X-Men occasionally clash with) are both immortals from the days of the Roman Empire, with the latter being stated as having been the very last Roman emperor before the empire itself collapsed. Wolverine villain Romulus and his sister Remus might also be Roman immortals; Romulus has claimed them to be such, though Remus later said he made it all up.
Another ambiguous case of this is Nightcrawler's father Azazel, who claims to have been alive since Biblical times. On the one hand, no hard evidence has been given for this claim, but on the other hand it hasn't been debunked outright either (unlike Romulus), so it could be true.
During the 90s an entire team of immortal mutants was established, the so-called Externals. A few classic villains were retroactively added to their ranks, but for the most part they were new characters, few of whom were particularly interesting. Between this and the obvious Highlander parallels, they didn't stick around long. Most of them were dispatched by Selene in an issue of X-Force, though they've since come back to life.
Perhaps the hardest-invoked of all in Marvel continuity is Selene, the External former Black Queen of the Hellfire Club. It's long been established that she's immortal, despite appearing to be in her mid-thirties at most. Turns out she's really 17,000 years old.
None of the above holds a candle to John Sublime. He is a sentient bacterium who's lived on Earth since the beginning of life on the planet, making him over 3 billion years old.
A Retconned case of this is none other than Moira MacTaggert, who was given a completely revised history in 2019's House of X story. Previously a Badass Normal and Token Human, she is now a mutant with Born-Again Immortality who lived at least one of her dozen or so lives to old age before she even met Professor X. While no hard dates are stated, this would appear to make her roughly about as old as Mystique and Destiny.
Most Fables are a few centuries old at least, but particular note goes to Pinocchio; it seems the Blue Fairy was a little too literal when it came to his wish. As he puts it, "I want to get laid!" He aspires to someday meet the over-literal fairy that granted his wish, so that he can "kick her blue ass". At one point, they blackmail a columnist who's threatening to expose the Masquerade by taking compromising photos of him with Pinocchio while he's passed out, then threaten to use them to "prove" he's a pedophile, so he'll delete his off-site evidence backups.
Ozma, the third leader of the Thirteenth Floor Sorcerers, looks about ten, but is centuries old, at least.
ElfQuest occasionally gets flack because of the slim, large-headed, waifish proportions of the centuries-old protagonists. This does occasionally get lampshaded in the plot; for instance, on one occasion Tyleet meets a human couple who can't believe she's old enough to be pregnant.
Arisia, a Green Lantern who originally appeared to be in her late teens (at the oldest) and who had a romantic relationship with Hal Jordan, was recently revealed to be several hundred years old and a member of a species that ages much slower than humans. This was a retcon to lower the Squick factor; originally there was a plotline where her feelings for Hal, combined with her power ring, caused her to go through puberty ahead of time so that she could appear to be of acceptable age.
Wolverine's healing factor also slows his aging; he was born in the late 19th century and fought alongside Captain America in WWII.
Captain America: Because of his unique physiology, when Steve Rogers took a dip in the ice for an indeterminate amount of time (from the the late 1940s to whatever time period he happens to step out into, usually "Present Day") while he became chronologically decades older, his body did not age since it was effectively cryogenically frozen and he still appears to be a man in his early-to-mid-thirties (depending on the artist). Arcs where Steve has the Super Soldier Serum removed from his body show him fully aged for all the years that have passed.
In his take on The Eternals Sprite is the ONLY child Eternal, and he's ticked off enough about it to set off the train of events that turned all the Eternals into ordinary humans and made everyone forget they ever existed. He's particularly ticked that Sersi has slept with every male Eternal except — guess who?
Several characters, including Mad Hettie and Hob Gadling, are otherwise normal humans who live for several hundred years.
Several of the Endless, those of human appearance, that is. For example, Morpheus and his sister Death, along with their estranged brother Destruction. All three have been around since the beginning of time, yet none look older than late thirties or early forties. Death in fact looks like she is still in her twenties (supposed to appear about sixteen, at least according to Gaiman's original idea of her).
The witch Thessaly (later known as Larissa) is several millennia old and one of the last of her kind, but looks to be in her late twenties or early thirties.
Shivering Jemmy, who is a Lord of Chaos (and therefore presumably pretty old), but takes the form of a little girl in clown make-up.
In Marvel's old Conan the Barbarian-continuity, the necromancer Thulsa Doom has been around since before the Valusian era. Although visibly undead, this should still make him a rather extreme example, as it means he's well over 20,000 years old.
Vandal Savage was born in roughly 50,000 BC. He's an immortal caveman who's spent his time with world domination plots. And he invented cannibalism.
A Star Wars Expanded Universe comic set in the Clone Wars introduces us to Fay, a centuries-old Jedi who understands the Power of Love and has used it to end and prevent wars, doesn't use a lightsabre and doesn't need to, is kept from physically aging past her twenties by her strong connection to the Force, and who if she hadn't given her reserves of Force energy to Obi-Wan to allow him to escape would have recovered from a fatal lightsabre wound. If not for her Heroic Sacrifice Fay would have lived forever. Let us hope she joins the ranks of Expanded Universe characters with action figures.
Fay's sacrifice has consequences far beyond saving Obi-Wan. Details here.
The Anzat is a race of vampiric creatures that appear from time to time in the novels, who can live upwards of 900 years or so. Their society is so ancient, their history predates the Jedi and the Sith, and while they prefer to feed on Force-sensitive creatures, they don't call the Force by that name; they consider that a term that younger races use for it. (They usually call it "luck" or "Sea of Memory" if they want to be fancier.)
Several characters from The League of Extraordinary Gentlemen series fulfill the trope, at least in later installments of the comic, such as Black Dossier. Mina Murray is given immortality by her encounter with Dracula, Allan Quatermain is rejuvenated after bathing in a pool of eternal youth, and Orlando is millenia-old and has changed his sex numerous times during the centuries. None look older than their late thirties; in fact, only Quatermain even comes close to looking even that old.
The Shade, of Starman fame, was born sometime in the early 1800s, and hasn't aged since the event that gave him his powers. His potential futures see him living for millennia to come.
Ra's al Ghul looks to be about in his 50s, but is really over 600 years old. This is due to his continuous revivals in the Lazarus pits (magical pools of... stuff... that can restore the dead to life).
His daughter Nyssa Raatko is similar, having been born in the 19th century and used a Lazarus Pit to keep herself young.
Alpha One of The Mighty looks like he is in his twenties but he had been operating since he appeared in 1952. It turns out that he's much older than that. He is an alien who had been around since the Revolutionary War.
Knuckles The Echidna and Chaos in Sonic the Comic was alive during the great war between the Echidnas and the Drakons which happened over eight thousand years ago.
Sonic the Comic Online! adds Tikal The Echidna who was sealed with Chaos, Vichama the God of Death and the reason Knuckles The Echidna is immortal as well as a weapon by the Drakon Empire called Shadow The Hedgehog and the advanced Guardian Robot called the Gizoid.
The vast majority of the depictions of Superman in any future time period show that he - and otherKryptonians - age significantly slower than humans do.
In the Elseworlds tale Superman & Batman: Generations he fits this trope, with Batman and Superman's granddaughters getting in on the act as well (in fact, one of his granddaughters is stuck in her early teens for over a century before finally getting it fixed so that she can age to adulthood.)
In The Third Kryptonian, Karsta Wor-Ul looks like a fit fifty-years-old woman, but she's been alive for hundreds of years.
ClanDestine: Adam Destine is about eight hundred years old and looks more like twenty, having been granted Complete Immortality by his beloved, the djinn Elalyth. Their children do age, but very slowly, so the older ones count for Long-Lived. Gracie, for example, is four hundred and looks about sixty or seventy.
The Authority: Jenny Sparks from the Wildstorm universe looks like she's in her 20s, when she's actually over 100, which gets repeated a lot. She's the spirit of the 20th Century, and eventually gets rebirthed into a new form as the spirit of the 21st Century to repeat the process again.
Solomon Ravne is suggested to be around 300 years old and must keep up his more youthful appearance through ritualistic Blood Baths and other forms of the The Dark Arts.
Ethan Kostabi is in fact a 2000 year old angel who fell to Earth.
Christian Walker from Powers is revealed to be a proto-human hominid that has evolved over tens of thousands of years into a modern human with super powers. Most of which he can't remember. There's hints that many of the major super beings in the setting may also have extremely long lives, or be part of an ongoing reincarnation cycle that brings those powers back again and again.
Most of the Demon Knights have some form of semi-immortality that has slowed down their aging process, and thus most of them are at least several hundred years old. The sole exception is Al Jabr, who is entirely human, and thus ages accordingly.
Klara Prast of the Runaways is a bit of a variation. She was born sometime in the late 1890s, but traveled forward a hundred years in 1907, when she was about 11 or 12, so she's still, according to Marvel's Sliding Timescale, not quite in her teens. A more straightforward example from the series would be Topher, a vampire who was born around 1900 and was turned when he was 17. He lived to be over 100 years old before he was stupid enough to try and feed on Karolina Dean, whose blood is infused with solar energy. There's also Forget-Me-Not, a villainess encountered by the Runaways when they were stranded in 1907. She boasted that men had been fighting over her for centuries, although whether or not this was true is unrevealed.
A group of The Knights Templar (Kenneth Irons, Gerald Irons, Sir Renaud de Gaudin and one other person) from Witch Blade became immortal by drinking from the Holy Grail. There is also former Witchblade wielder Katarina Godliffe, who lives in the Faerie realm where time flows differently, allowing her to live to the present day, and The Survivor, who was born in the universe before the currect one.
Wonder Woman (1942) (Vol 1): In the Golden Age the Amazons were women who had arrived on Paradise Island through various means throughout history since Antiquity and had chosen to remain there, taking an oath to uphold the Amazons' ideals on peace and justice and drinking from the fountain of youth to maintain their longevity after undergoing training to allow them to survive drinking from it. Most of the Amazons are well over 1000 years old but few look to be over 50.
Wonder Woman (1987) (Vol 2): The Amazons date back to Ancient Greece, and aside from Wonder Woman, their population hasn't increased in the 3000+ years of exile - they still look between twenty and forty years old. Elseworld stories show this applies to Wonder Woman as well.
The Legend of Wonder Woman (2016): Most of the Amazons are mortal with normal human lifespans, but a small handful including Diana's mother opted to become champions to members of the Greek pantheon and stopped aging back in the Bronze Age, and still look like they are in their twenties at the time of the comic in the twentieth century.
Mia of Death Vigil, who usually looks like a teenage girl, has been around for at least a few centuries. Given that she's referred to as a "primordial," she's presumably quite a bit older than that.
Number Five from The Umbrella Academy is an eighty-year-old man trapped in a ten-year-old's body. There's no telling how old he really is, however, as his aging was halted by The Temps Aertanalis.
In Athena Voltaire and the Isle of the Dead, the reason that de Vargas knew where to find a 400-year-old shipwreck is that he was personally present when it was made, and has spent the intervening years getting to the point where he can return.
Atrea from Ultimate Fantastic Four is somewhere over a thousand years old, but looks no older than her mid-twenties.
In Warlord of Mars, Martians are explicitly said to not age once they reach maturity, nor do they die unless slain. Flashbacks reveal that many characters such as Dejah, Thuvia and Woola have lived for at least centuries before John Carter arrived on Mars. That doesn't seem to be always the case, as there are many elderly-looking Martians such as Issus and Tardos Mors.
The Pureblood vampires in Blade age extremely slowly (turned vampires don't age at all). Charlotte looks to be about 12, when she's actually around 200. Overlord Rusk appears to be an adult man and is actually 600.
While characters in Transformers being millions of years old for a start is nothing new, in The Transformers: More Than Meets the Eye, the tiny archivist Rewind is mentioned to be old enough to remember before Nova Prime came to power, making him at least nine million years old. For the record, that's the same given age as Kup, and yet Rewind neither looks or acts anywhere near as old as him.
Similarly, over in The Transformers: Robots in Disguise, Arcee is also a good nine million years old, having been active in the second Cybertronian war. She also doesn't show any signs of her age. Later reveals in the comic show she's somewhere over twelve million years old, making her the oldest character in the story (not counting Kup, and he had to use time-travel to cheat). Unlike Rewind, she does act like it.
Backlash was born in Atlantis back before it sank, some three-thousand years ago.
Angel Catbird: Neferkitty was alive in Ancient Egypt, as she was in fact Queen Nefertiti. Her actual name is Neferkitty, and Nefertiti came about from a translation error.
Count Catula was a cat in medieval times, and became a vampire after being bitten by Count Dracula.
Monstress: The Ancients and the Old Gods are practically Time Abysses, having been around for all of recorded history. Maika's father the Lord Doctor claims to have hosted Zinn for 500 years before passing it to her, but it's unclear if that's an Arcanic trait or a benefit of containing a Monstrum.
Troll from Youngblood is thousands of years old, however much he'd like to keep it a secret.
The titular character of Sasmira is over 4000 years old. She was the illegitimate daughter of a Pharaoh in Ancient Egypt, and was cursed with immortality for reasons unknown to Prudence. It's revealed in the third book that a priest cursed her because she refused his advances.