You might be interested in emperor Justin I (518-527), who was an illiterate Illyrian peasant who went to Constantinople to join the army, eventually becoming the head of the imperial bodyguard. After the death of emperor Anastasius, various palace factions plotted to put their candidates in power. According to one story, Justin was given a lot of money by another official to bribe the soldiers to back one particular candidate. Justin however cunningly used the money to bribe the bodyguards to proclaim himself emperor instead. This differentiated Justin from previous soldier-emperors who used their armies to seize power, since Justin was both a good soldier and an excellent political operator. The fact that he remained illiterate is another remarkable fact, since despite this obvious barrier he seemingly ruled rather well, as his reign set the stage for the more eventful reign of his nephew Justinian, who was also born a peasant but brought to Constantinople by his uncle to be groomed as his heir. Procopius, a dissident against the regime, wrote about Justin in his Secret History in this fashion:
When Leon was holding the imperial power in Byzantium, three young farmers, Illyrians by race, Zimarchus, Dityvistus and Justinus from Vederiana, men who at home had to struggle incessantly against conditions of poverty and all its attendant ills, in an effort to better their condition set out to join the army. And they came to Byzantium, walking on foot and themselves carrying cloaks slung over their shoulders, and when they arrived they had in these cloaks nothing more than toasted bread which they had put in at home; and the Emperor enrolled them in the ranks of the soldiers and designated them for the Palace Guard. For they were all men of very fine figure. [...]
And when the Emperor departed this life, he himself, because of the power of his office, succeeded to the throne, being already an old man tottering to his grave, who had never learned to tell one letter from another, and was, as the familiar phrase has it, "without the alphabet," a thing which had never happened before among the Romans. And while it was customary for the Emperor to affix letters in his own hand to all documents containing the orders that issued from him, he was unable either to issue orders himself or intelligently to share in the knowledge of what was being done. [...]
But in order that they might have evidence of the Emperor's hand, those who had this matter in charge devised the following plan. Taking a small strip of prepared wood, they cut into it a sort of pattern of the four letters which mean in the Latin tongue "I have read," and dipping the pen into ink of the colour which Emperors are wont to use in writing, they would put it into the hand of this Emperor. And placing on the document the strip of wood which I have mentioned and grasping the Emperor's hand, they moved it and the pen along the pattern of the four letters, causing it to follow all the winding lines cut in the wood, and then went their way, carrying that kind of writing of the Emperor.
Such an Emperor had the Romans in Justinus. And he had a wife named Lupicina who, as being a slave and a barbarian, had been concubine of the man who had previously bought her. And she as well as Justinus attained the throne in the closing years of life.
You could look at some liberti (ex-slaves), perhaps: for instance, Horace's father was a freedman, which may have hindered his social mobility, but certainly not that of his son's.
As I always disclaim, I'm no classicist, but your question reminded me of a review by Mary Beard in the TLS a few years back: http://www.the-tls.co.uk/tls/public/article879727.ece. She mentions Horace, but also touches on contemporary nouveau riche perceptions of successful liberti, which I thought I'd quote her as a potential perspective you might be interested in:
... in treating Roman freedmen in this way, modern writers are partly (consciously or, more often, unconsciously) reflecting the prejudices of their ancient predecessors and sources. Historians in the Roman world certainly saw moral and political dangers in freeing too many slaves – most notoriously, Dionysius of Halicarnassus, whose history of Rome, written at the end of the first century BC, includes a rant about the slave criminals and prostitutes who used their ill-gotten gains to purchase freedom from their masters. And the most lurid caricature of a vulgar freedman comes from Petronius’s novel, the Satyrica, featuring the extravagant dinner party of the libertus Trimalchio – with its ludicrous luxury, its parodically expensive food, and hilarious discussion of proposals for a freedman’s elaborate tomb to rival that of Eurysaces.
As she adds, though:
... Never mind that this is an elite skit, written by a one-time friend of the Emperor Nero about a member the aspirant underclass; that hasn’t stopped generations of modern historians writing as if Trimalchio was a “typical” Roman freedman. In fact, in the eyes of many, the baker’s monument [see the beginning of her article for the context on this] provides nice confirmation of just how true to life Petronius’s Trimalchio was.
Ooh something I know about! I'm not sure about the best example of rags to riches, but there is the great charioteer Gaius Appuleius Diocles.
Between 122 to 146 AD Diocles won 1462 times in 4257 races until his retirement aged 42. His longevity is notable as charioteering was a very dangerous sport, the circus maximus was frequently a scene of tragedy as charioteers were crushed against the wall or lost a wheel. That isn't to say Diocles raced like Sebastian Vettel from the front as the greatest portion of Diocles' victories (1064) came from prestigious one-on-one races against the best charioteers from opposing stables, winning during the final stretch in one third. Diocles was also known for performing tricks for the crowd, most notably managing to race 7 unyoked horses to victory, winning 50,000 sesterces.
The one-on-one races also happened to be the best paying races, Diocles amassed 35,863,120 sesterces. Adjusted for inflation, that is roughly $15,000,000,000 making him arguably the best paid athlete of all time. Diocles' riches were such that he could pay for the entire city of Rome's grain for a year.
Sources: http://fd.valenciacollege.edu/file/gadams/romanCharioteer.pdf http://www.lqbeta.org/roundtable/roundtable/greatest-of-all-time.php
Perhaps Galen would fit this story. He was a greek man without citizenship, and practiced medicine and healing on gladiators (gruesome business), but was eventually appointed to be the private physician of Emperor Marcus Aurelius, then later his successors.
A chance to comment on the inspiration of my reddit name!
Maximinus Thrax was very low born but rose to become emperor of Rome in 283 CE. I'm lacking sources right now, but you read the wikipedia article.