Different societies responded to arming slaves in different ways. You seem to be interested mainly in chattel slavery involving people of African ancestry in the Americas, so I'll confine my response to that context.

In the antebellum U.S., there was a stigma associated with arming slaves, but it was a topic that was debated in times of war. Here, for example, is a letter from Confederate officer Patrick Cleburne in 1864 suggesting the arming of slaves. In general, though, this did not happen. Most states had traditions of prohibiting blacks from carrying arms, and particularly after the Haitian Revolution (1791) and Nat Turner's Rebellion (1831) there were widespread fears of slave rebellions in southern territories. There were exceptions, though; Rhode Island formed a regiment of free blacks and slaves during the American Revolution, and there were a few hundred black loyalists who fought for the British.

In Spanish America, though, there was a longer tradition of arming slaves and free blacks to fight for the crown. The colony of Florida had a long-standing black militia, and there was a similar precedent of arming slaves to defend Cuba from invasion. Many of these slaves and free blacks participated in the Latin American Wars of Independence in the early 19th century.

Historians have suggested several reasons for this difference. One theory is that binary race divisions (black/white) were much more stark in Anglo-America were much starker and more heavily enforced than they were in Spanish America. It was more imperative that racial power relations remained in place with whites at the top; arming slaves would muddle that framework and provide blacks with an avenue for armed resistance. Parts of that interpretation are problematic, however, because it overlooks the extent to which race identity was also rigidly codified in Spanish American society. There were dozens upon dozens of different castas (racial categories based on ancestry), each with their special place within the power structure, and negros were lowest on the spectrum. Additionally, Spanish colonial authorities found that granting arms to free blacks was a good way to solidify the institution of slavery, as free blacks were more inclined to fight in order to keep their social status intact vis-à-vis enslaved Africans. There are also arguments that Anglo-Americans didn't need to arm slaves, as there was a large pool of white men to draw on for military service, whereas in Spanish America that pool was much smaller.

In any case, why societies have responded differently to the issue of arming slaves is still a hotly debated historical question. The best recent book to check out in this regard is Arming Slaves: From Classical Times to the Modern Age. Though the time frame is much larger, there are essays in the collection that cover African chattel slavery. You can read a brief review of the work in the William and Mary Quarterly here.

The movie makes a case for a very strong relationship between the master and his major domo but, yes, it was generally against the law for masters to arm slaves under whatever circumstances & free blacks were generally denied their 2nd & 4th Amendment rights, so that searches of their houses could be organized without court order just to double and triple check that they didn't have guns. (Incidentally, this is a very prominent thread in Justice Thomas's excoriations of gun control).

Humans being humans, though, I'm sure there were some rare cases.

I had thought that land owners would send slaves to war in their stead or in support of the cause which would see them armed. Not really what you're looking for in the context of the movie, but as a strictly technical answer it would be yes.

edit: Learned some new stuff.