I am unsure of the details on some of these
Professor Ivo- This foe of the Justice League was a mad scientist. Besides building Amazo and other killer androids, he developed an immortality serum. It gave him many reptillian features, but did make him immortal.
Metamorpho- A normal human transformed by the Eye Of Ra (or was it Horus?). Besides the powers granted by his new form, he is immortal and appears to be extremely dificult to kill through violence. A woman (I don’t remember her name) was later transformed. She attempted suicide in many ways, but was unable to die.
Evil Star- A human (possibly from another planet, but still homo sapien) scientist with a death phobia. He developed a device which gave him power and made him immortal. It also made him thoroughly evil. The scientist is a good man, but his fear always makes him put the immortality ring on again.
Mutliple Man- Foe of the Challengers Of The Unknown, he discovered (a scientific serum? A mystic potion? Found a lost tomb?) that promised many lives. Each time Multiple Man seemingly died, he returned with a new set of powers.
Doctor Fog- IIRC This member of the Global Guardians is immortal, possesses great mystic powers, and cannot leave the mountain he dwells in.
The Baron DeWinter- Founder of Night Force (or was it Night Watch?), the Baron is immortal, posseses great mystical power, and cannot leave the mansion he dwells in.
Alan Scott- The union Scott has achieved with the mystical green flame allowed him, with no conscious effort, to make himself forty years younger and stop the aging process. He may well be immortal at this point.
General Immortus- Enemy of the original Doom Patrol, if he wasn’t immortal the name makes no sense.
Pronsias Cassidy-He’s a vampire. While Ennis deliberately left much of his view of vampires untold, it is clear that they do not age.
Mister E-The post Vertigo version. He has vast mystic powers involving time. He can travel through it(both backwards, or just at a much higher rate than the rest of us), stop it, and reverse it. On at least one occasion, he has used the last ability to make his death unhappen after being killed in battle.
Phantom Stranger- The Secret Origins featuring the Stranger lists a fourth origin. Without spoiling, this one says that he was once an ordinary human who gained immortality through a scientific\mystical accident.
IBAC- IIRC This joe average wanted power and immortality. He made a deal with the devil and got it. When he said IBAC (Ivan the terrible,? , Attila the Hun,?) he became a powerful villain.
Black Adam- He’s been around since anient Egypt. Doesn’t show any signs of aging.
Shazamo- Not to be confused with the wizard Shazam (who doesn’t count because his physical body is very dead), this wizard was Shazam’s student. Then he turned to evil. He was cursed with goat’s hooves. His magic cannot harm women. He seems to be ageless and immortal, probably through his own magic.