Slaves became a core component of the increasingly powerful Roman economy from the 2nd century BC, utilised in large numbers in mines and working the latifundia, huge agricultural estates, but as we all know they were also heavily used in domestic situations, businesses and in the entertainment industry (Dillon & Garland 295-6). Slaves had different experiences and prospects depending on what sort of job they did, where they did it, and who they worked for. However, as we might expect, aside from major revolts (which I won't go into) evidence exists of very common resistance by individual slaves in the form of "shirking, vandalism, petty theft, and running away." (Morley 315).

While they could run, they could also be recaptured. Those with a tendency to run often ended up with a slave collar (296). We have some fascinating evidence on escaped slaves from several sources. I'll quote them here, from pages 321-2 of Dillon & Garland:

This first one is just a small extract, but it gives you the gist of what recapturing slave might involve in terms of punishment and future prevention:

"...when I bring him back home like a runaway in manacles and a dog-chain and dog-collar" (Lucilius 29.917-8)

This second quote is from a road milestone recording the achievements of either Publius Popilius Laenas (consul 132) or T. Annius Rufus (consul 128).

"..Also as praetor in Sicily I sought out the runaways belonging to men from Italy and returned 917 people. " (ILS 23)

This third quote is by Cicero, writing to his friend P. Rufus:

"I beg of you with more urgency than usual, in view of our friendship and your continual devotion to me, that you particularly exert yourself in the following matter: my slave Dionysius, who had charge of my library which is worth a great deal of money, stole a large number of books and, believing he would not get away with it unpunished, ran away. He is in your province. Both my friend Marcus Bolanus and many others saw him at Narona, but they believed him when he asserted that I had manumitted (freed) him. If you should see to returning him to me, I can't tell you how grateful I would be. It is a small thing in itself, but has made me very upset. Bolanus will tell you where he is and what can be done. If I should receive the fellow back through your agency I shall consider that you have done me a very great favour. *(Cic. Ad Fam. 13.77.3)

Cicero was not unusual in having issues with slaves like this: Cato the Elder apparently had similar issues (Cato On Farming 2.2-4, 7), and Cicero had had other runaways. As far as we know, he did not get Dionysius back (321). While the quote further above from a Roman magistrate tells us that a praetor might do some slave-catching, there was apparently no state apparatus for helping owners recover their slaves, and we can see from Cicero's letter that it was up to the master's resourcefulness and contacts to do most of the work if he could not get someone like a praetor to help him. It is important to note however that slaves could be recaptured, as apparently a Sicilian praetor managed to return 917 such slaves in about 3 years (that's about how long Gaius Verres governed Sicily, so I'm assuming that was normal). When they were recaptured, there was basically no limit to the punishments the dominus could inflict or measures he could take to prevent future escapes, so to run away cannot have been a decision made lightly. Intelligent and educated slaves like Dionysius however, who could claim he was freed and might have been able to produce some sort of bogus documentation supporting such a claim, no doubt had better chances. But if they were caught, assuming they were allowed to live, they could easily end up like our unfortunate from Lucilius, who ended up wearing manacles and a dog collar, or worse. And you'd better bet your master will look for you if you're a fugitive slave: one of the few reasons a Roman legionary in the Republic might not be punished for leaving a camp without leave was to pursue an escaped slave. Any dominus, who may have gone to some effort to get their slave back, would take whatever measures he feels necessary to ensure it doesn't happen again. For many slaves, it was probably less worry to stay where they were.

Sources:

Ancient Rome: From the Early Republic to the Assassination of Julius Caesar (sourcebook), Eds. Matthew Dillon and Lynda Garland, New York: Routledge, 2005.

Morley, Neville, "Social Structure and Demography" from A Companion to the Roman Republic, Eds. Nathan Rosenstein and Robert Morstein-Marx, Oxford: Blackwell, 2010, 299-323.

Followup question: Did slaves in the Roman Empire count as a member of the population? Or did they partially count them in a system similar to the US's Three-Fifths Compromise?

On the other side, wouldn't there be a list of who owned what for taxation purposes (for example, from the census)? Wouldn't that list not only physical property but also slaves?

If I can ask a related question, I've seen in some cultural depictions that effectively anyone captured in war could be taken as a slave, was that the case? If so what was to stop a soldier capturing a random roman civilian?