If you killed the Caesar, would you become the new ruler, or would the heir to the throne become the new ruler and toss your ass in the dungeon?
A friend of mine says that if a person kills the Caesar, he gets to be Caesar. I think that would have a lot of problems with people constantly challenging the throne. What’s the truth?
Short answer: no.
Long answer: it depends.
While there was no Roman law or tradition that decreed the person who killed the reigning Caesar would automatically assume the throne, in practice this did happen on more than one occasion. However, the usurper usually had the backing of either the army or some significant political faction, or both.
Roman emperors who were killed in office succumbed to any number of murderers: family members, political rivals, slaves (probably induced to kill by family members/political rivals) military leaders, etc.
Much as with the “rules” of succession in the Soviet Union during the Cold War, it had more to do with who you could count on to watch your back once you claimed the throne than with any legitimate right to succeed.
Slightly off-topic example of how ridiculous things got: Upon the death of the emperor Pertinax in 193 A.D. there was no clear successor. In the confusion, a man named Didius Julianus became emperor (albeit briefly) when he promised the largest bribe to the Praetorian Guard (the emperor’s body guards). Effectively, he outbid his opponent and bought the throne.
He ruled for all of two months before a provincial governor named Septimius Severus claimed the emperorship, marched back into Italy, won over the Praetorians, and had Julianus executed.
Two words: I, Claudius.
aesop is correct. Usually (but not always) the person who assassinated a Roman emperor WAS a man with some sort of claim to the emperorship (a political rival, military general, etc). Only such a man would have the power AND motive to kill such a powerful head of state. However, one did not automatically succeed a murdered emperor to power solely because one killed him (ie, it didn’t work like a boxing championship belt).
In fact, if I recall correctly, the murders of Gaius Caligula WERE executed by his successor Claudius, as Bear Nenno alludes to in the OP.
It should be noted, however, that the emperor possessed the title “Augustus”, not “Caesar”. “Augustus” was roughly equivalent to “king”, while “Caesar” was roughly equivalent to “prince” or “heir to the throne”.
In the interests of completeness, it should be noted that, in aesop’s historical example above, Septimius Severus had to fight not only Didius Julianus, but two other rivals, Pescennius Niger and Clodius Albinus, as well.
He “won over” the Praetorians with the not inconsiderable help of his army. Thus his recommendation to his sons: “Cherish each other, enrich the soldiers, and despise the rest”.
Re: I, Claudius. In my humble opinion, this was the greatest miniseries of all time. However, it was historically inaccurate, much like Braveheart. Specifically, Livia was almost certainly guiltless of all her alleged crimes: she certainly did not have the power to kill Gaius and Lucius, and there’s no solid evidence to suggest she assassinated Agrippa, Marcellus, Postumus Agrippa, or Augustus. She also did not have the motive–in real life, Augustus had no plans to replace Tiberius as his heir, and, indeed, shared power with Tiberius as Augustus grew old.
Caesar meant nothing like ‘prince’. Caesar was a family name. It was adopted by some succeding emperors (imperatori) in order to establish a sense of connection to the family that held the claim to being emperor the first several times (ending with Nero).
Augustus was not a title, either. It was a descriptive name. Eventually, IIRC, it may have obtained some legal connections (those with access to better descriptions of later Roman law to explain; the ‘office’ of princeps which was Augustus Caesar’s basis for legally ruling the empire was a quite confusing legal entity, hiding as it had to the concept of a supreme ruler under the cloak of a republican governmental structure). Augustus explained the basic relative status of the emperor as one who had divine connections, compared to the rest of humanity (humanus). Many succeding rulers of Rome also adopted the description Augustus.
Among other titles held by Augustus Caesar (formerly Octavian) were Pontifex maximus (chief priest of the state religion) from 12 B.C., and pater patriae (father of the country), from 2 B.C.
The Roman governmental form after the mess created by the dictatorship of Julius Caesar is an interesting read, for anyone who thinks WE have weird politics… 
Now, as for who succeded whom to the emperorship:
For the first roughly 200 years, the title of princeps passed mainly to designated heirs. Thus, Augustus to Tiberius, Tiberius to Caligula, Claudius to Nero. This is not to say that murders weren’t common, for example, the murder of Caligula and the elevation of his uncle, Claudius, who nevertheless was NOT the instigator of the murder. Nero committed suicide rather than have the angry Senate execute him; he was succeded by Galba, who was in rebellion against him. Galba was executed by the Praetorian Guard, who favored Otho; there were at the time of his death actually three claimants to the emperor’s throne, Otho, Vitellius and Vespasian. Otho committed suicide in the face of the advancing forces of Vitellius; Vitellius was murdered by his own troops as Vespasian advanced on Rome.
Vespasian was succeded by his sons, Titus and Domitian (Titus first, who was heirless, then Domitian). Vespasian probably is the first of the true emperors, that is, men who ruled and had legal sanction to be the sole ruling authority; certain powers granted to Vespasian were never previously (so far as we know) granted to prior emperors. Domitian was murdered by a conspiracy in the Praetorians; Nerva, his successor, was not his heir and may have participated. Nerva’s adopted son Trajan succeded him, Trajan’s adopted son Hadrian (who built a wall) succeded him, Hadrian adopted Antoninus, and forced Antoninus to adopt Marcus Aurelius; the succession went as planned in each case without murder, etc. Commodus, his true son, succeded him in 180 A.D. So, as you can see, for the first 220 years of autocratic rule by the Caesars (beginning with Augustus in 27 B.C.), there were very few instances of someone being killed, and in only two or three cases did the successor have a hand in the killing, though arguably Galba, Otho, Vitellius and Vespasian all became emperor by making war upon the established emperor.
It was only after Commodus’ reign that things started to slide downhill. Commodus’ murder was follwed by civil war, and thereafter come many of the instances we think of when we think of the office of princeps being the prize of murder.
DSYoungEsq–I agree that Caesar and Augustus were not originally titles roughly equating to “prince” and “king”, and were instead, as you correctly maintain, a family name and a title. HOWEVER, with the passage of time, the emperors did indeed use Augustus and Caesar as titles meaning “prince” and “king”, at least on coinage:
http://www.bitsofhistory.com/info/r_titles.html
It should also be noted in your chronology that Marcus Aurelius had a co-emperor, Lucius Verus, who ruled jointly with him from 161 to 169 A.D. He was not nearly so significant a ruler as Marcus Aurelius, however.