There's a very detailed answer to this in the FAQ by /u/sowser
TLDR: No, American slavery was an inherently racial system. While some other forms of semi-free labor (such as indentured servitude) existed, legal slaves were exclusively of African descent.
If you're asking specifically about slavery of whites, like the false notion of "Irish slaves", you could read previous discussions here by /u/Irishfafnir and /u/sowser .
For native Americans / Indians, they were, in quantity. A good start is here , where commiespaceinvader pointed to answers by anthropology_nerd, and silverappleyard pointed to answers by Dire88.
As for Asians, I hope more is written: the only previous discussion I can find is "How did Asian Americans treat African Americans during the slave trade?" , but it's brief, and /u/ParkSungJun cites counterexamples to Adeptpotato's statement.
This is not to discourage discussion. More questions, data, and debate are welcome.
There is much talk here about American Indians/Native Americans being enslaved. It’s worth noting that many slaves in the antebellum era had some native ancestors (the slaves were considered black/African due to notions such as the “one drop rule”). But “Indian slavery” really declined in the South after the Yamasee War (1715-1717). Prior to this, Indian slaves were commonly used in the South, especially South Carolina, the hub of the Indian slave trade. The slave trade relied on “slaving” tribes to take captives from other tribes and sell them, most of these slaves ending up in the West Indies but a significant quantity remaining enslaved on plantations in the Southeast. However, Indian resistance to this enslavement manifested in the Yamasee War where several southeastern tribes fought back against colonial power in SC. Their societies had been upturned due to the various calamitous effects of the slave trade, and though this coalition didn’t win the war, hundreds of white settlers were killed which certainly called into question the viability of enslaving Indians. At this point the emphasis truly shifted to African slavery, there already being pervasive ideology to support the notion that blacks were uniquely suited for enslavement. Southeastern Indians in the antebellum era were regarded as “free people of color,” legally speaking, but couldn’t be enslaved (though the labor they performed often resembled the “hiring out” slave system). There are antebellum accounts of Eastern Cherokee people being abducted and taken to be sold in Charleston, but being saved when their true ancestry was proved. In summary, American Indians were not enslaved in the South in any significant quantity in the antebellum era, I just wanted to clarify the chronology.
Sources: Slavery in Indian Country: The Changing Face of Captivity in Early America by Christina Snyder
From Chicaza to Chickasaw: The European Invasion and the Transformation of the Mississippian World, 1540-1715 by Robbie Ethridge