The cusrus honorum, or course of honors, was the sequence of elected offices, or magistracies, which could be held. It seems to have been customary since the early Republic, but in 160 BC was written down as law.
The numbers in parentheses represent number of the office in the late Republic. Those in bold are part of the standard cursus honorum for rising politicians.
(1) Dictator- A sole leader, appointed by the Senate in times of crisis to rule for a period of no more than six months. As his second in command, he would choose for himself a 'master of cavalry' As this was a command of exceptional power only used when absolutely necessary, it is not truly part of the cursus honorum.
(2) Censors - The main duty of the censors was to act as the registrar of Rome , and therefore oversee the public census. The true power of the censor, however, lay in his ability to oversee the enforcement of public morality. He could cause equestrians and patricians to lose their rank, and even remove a senator from office. Due to the potential power of of the censor, most achieved this rank only after they had already become consul, thereby already proving their good character.
(2) Consuls - They were always two in number, and elected yearly in order to limit their power. They had imperium, the ability to command the armies of Rome. They presided over the senate, and enforced its legislation. At the end of their term, they would typically serve as a proconsul, where they would often govern an important province with its own military forces.
(8) Praetors - Originally, the term praetor was used to designate those with imperium, and so referred to the consuls. As Rome grew, however, the need for more judges arose. The office of praetor was created, but originally there was only one. The number grew with the size of the empire, and Sulla eventually settled the number at eight. The primary duty of the praetor was to act as a judge. Like the consuls, they also possessed imperium, though they seldom were called upon to use it. When there term was over, they were sometimes appointed as propraetors. While technically this office was open to all men, members of the plebeian class rarely rose this high on the cursus honorum.
(4) Aediles - These men oversaw the public games held in Rome. Each year, two were required to be elected from the plebeian class, and two usually came from the patrician class (called the curule aediles). Although it was not required to become aedile to achieve the rank of praetor, it was highly beneficial for a patrician to so. It was an easy way to curry favor with the people, if during his year in office he held magnificent games. For plebeians, this was as high an office as could normally be held.
(10) Tribunes - This office was created to protect the rights of the plebeian class, and so all elected Tribunes were required to be of that class. First created during the early Republic, they had the extraordinary power of veto (in Latin, I forbid) over any action of the Senate. The office of Tribune was considered sacred, and so anyone who harmed one would immediately be put to death.
(10) Quaestors - Originally there were only four, but in the fifth century the number was raised to ten. This was the lowest office on the cursus honorum. They were in charge of the running the treasury in Rome, as well as the public records.