84-65 (tie). Titus (died in AD 81), Nerva (98), Trajan (117), Hadrian (138), Antoninus Pius (161), Marcus Aurelius (180), Septimius Severus (211), Tacitus (276), Constantius I (306), Gallerius (311), Constantine I (337), Constantius II (361), Theodosius I (395), Arcadius (408), Constantius III (421), Honorious (423), Marcian (457), Libius Severus (465), Olybrius (472), Leo I (474): Natural causes.
64. Vespasian (79): Natural causes; quipped "Uh oh, I think I'm becoming a God" as he died.
63. Diocletian (311): Abdicated voluntarily, lived for six more years in his vast palace compound tending to his vegetable gardens before dying of natural causes.
62. Romulus (~500): Forced to abdicate, sent off to live in Campania with a nice pension, presumed to have died of natural causes decades later.
61. Glycerius (480): Natural causes, after being deposed and forced to become a bishop.
60-59 (tie). Augustus (14), Claudius (54): Probably natural causes, though both were rumored to have been poisoned by their wives.
58. Lucius Verus (169): Food poisoning.
57. Jovian (364): Suffocated in his rooms by carbon monoxide fumes from a charcoal grill. Alternatively, may have eaten some bad mushrooms.
56. Theodosius II (450): Fell off a horse.
55. Claudius II (270): Plague.
54. Valentinian II (392): Discovered hanged in his palace; may have committed suicide because he was dominated by his chief general and had no real power, or may have been murdered by said chief general.
53. Tiberius (37): His entourage thought he died of old age, announced his death, then smothered him in a panic when he suddenly regained consciousness.
52. Nero (68): Tried to commit suicide as his regime collapsed; after several failed attempts, he ordered his private secretary to stab him in the throat.
51. Domitian (96): Stabbed to death by a large group of palace officials.
50-46 (tie). Caligula (41), Pertinax (193), Elagabalus (222), Balbinus & Pupienus (238): Assassinated by members of the Praetorian Guard.
45. Alexander Severus (235): Assassinated by mutinous soldiers in a coup.
44. Constans (350): Assassinated while seeking refuge from coup plotters in a temple.
43. Carinus (285): Assassinated by an officer whose wife he had seduced.
42. Caracalla (217): Murdered by one of his bodyguards while urinating on the side of the road
41. Numerian (284): Possibly assassinated by one of his officials while on campaign against Persia; his rotting corpse was carried in a closed coach for hundreds of miles across Asia Minor before his death was acknowledged.
40. Aurelian (275): Murdered by high government officials who had been shown a forged document indicating that the emperor had marked them for execution.
39-36 (tie). Gordian II (238), Philip the Arab (249), Maxentius (312), Constantine II (340): Died in battle in civil wars.
35-32 (tie). Macrinus (218), Severus (307), Licinius (325), Gratian (383): Executed after losing civil wars.
31-30 (tie). Avitus (457), Julius Nepos (480): Lost a civil war, were both forced to become bishops, then starved to death (Avitus)/stabbed to death (Julius Nepos).
29-26 (tie). Otho (69), Gordian I (238), Maximian (310), Maximinus II (313): Committed suicide after losing civil wars.
19-25 (tie). Didius Julianus (193), Maximinus Thrax (238), Trebonius Gallus (253), Aemilianus (253), Gallienus (268), Florianus (276), Probus (282): Murdered by their own soldiers during a civil war.
18. Quintillus (270): Accounts differ: Murdered by his own soldiers because he was too strict, or maybe died in battle in a civil war, or maybe suicide.
17. Gordian III (244): Died while on campaign against the Persians, possibly in battle.
16. Decius (251): Died in battle against the Goths.
15. Julian (363): Died of hemorrhaging three days after receiving a spear wound in battle against the Persians.
14. Carus (283): Possibly struck by lightning.
13. Valentinian I (375): Became so angry at German ambassadors who were not sufficiently deferential that he suffered a rage-stroke.
12. Valentinian III (455): Murdered by soldiers who had been paid to do so by a senator whose wife Valentinian had raped.
11. Leo II (474): Poisoned by his own mother so her husband could become emperor.
10. Geta (211): Murdered in his mother's arms by soldiers on orders of his brother and co-emperor
9. Commodus (192): Given poison by conspirators, but he vomited that up, so they brought in a wrestler to strangle him in the bathtub.
8. Vitellius (69): Dragged from hiding as his regime collapsed, strangled, then ritually thrown down a flight of stairs.
7. Valens (378): Wounded in battle with the Goths, he was carried to a small hut, which the Goths later burned down, unaware the emperor was inside.
6. Petronius Maximus (455): Fled Rome rather than staying to fight invading Vandals; stoned to death by an angry mob of Roman refugees.
5. Majorian (461): Deposed, tortured, and decapitated by his chief general.
4. Anthemius (472): Lost a civil war with his chief general, fled to St. Peter's Basilica for refuge, was dragged out and beheaded.
3. Galba (69) Murdered by calvary officers in a coup; severed head brought to his successor's supporters, who carried it around and mocked it.
2. Joannes (425): Captured after a civil war; after his hand was amputated, he was paraded on a donkey and subjected to insults, then decapitated.
1. Valerian (sometime after 260): Captured by the Persians and died in captivity; rumored to have been used as a human footstool by the Persian king, killed by having molten gold poured down his throat, then taxidermied.
Josh Fruhlinger quit five semesters into an ancient history Ph.D. program, but that's still five semesters more than most people do. He has a Tumblr and a Twitter and runs the number one Mary Worth fan site on the Internet.