I know that the 'Christopher Columbus proved Europe wrong about the Earth being flat!' thing is blatantly false, I also know that Greek scientists discovered it many, many years before and it was the commonly accepted model among scientists for many centuries after that, but what about the common people? I know the Printing Press existed for about 50 years after Columbus 'proved' it was round, but before then when books weren't as widely published or available, would the common people (Of any variety--Roman citizens, Peasants, etc. Basically, people who weren't scientists and philosophers) have known that the Earth was round?
This has been covered in a number of recent threads. Here is the most recent I recall. Similarly, to quote what I wrote in the last one that I responded to:
As with jschooltiger, I shouldn't like to say that it is categorically impossible that someone may have feared [that they would sail off a flat earth] (after all, I've not evaluated the source material myself on this point). But it seems unlikely in the extreme. As the links below note (I've also written about this before on here also), we have no evidence of any educated person after the 6th century arguing that the earth is flat. Furthermore, we have no reason to suppose that it was a popular belief among the uneducated, and at least some tangential evidence to suppose that it was a belief that was taken for granted in things like sermons. Also, for this period in particular, we actually have an extant globe from 1492, finished before Columbus returned from his voyage, which notably doesn't have an american continent in the ocean separating Europe and Asia.
Though the most useful answer on Askhistorians that I'm aware of will likely be this response by /u/jschooltiger.
I assume you're referring to how common this knowledge was in Europe, but it was also a well-known problem for Muslim astronomers and mathematicians because a spherical earth has direct ramifications for the qibla, the direction of prayer towards Mecca. The direction one ought to pray in is, ideally, the shortest distance between those points which involves some (for the time, and for a mathematical laymen like myself) rather complex trigonometry imposed upon a spherical globe.
The ultimate solution was to compile a table calculating the qibla for all longitudes and latitudes, which was done in the 14th century (AD) by the Syrian astronomer al-Khalili.
I can't say whether it was something "common folk" were actively conscious of, but as a result virtually any Muslim who prayed in the Middle Ages was doing so according to a directional line that was calculated for a spherical earth.
There are exceptions, and in practice even once the mathematical theory had been resolved, the ability to actually determine one's own latitude and longitude in the medieval period was inexact, among other reasons why the Qibla might not be accurate.
For more on this see the Encyclopaedia of Islam entry on the subject "Kibla".
Just as a followup to this question, would anyone have any resources about what the Asian section of the world thought when it came to the Earth being round or not? From what I know, in Ancient China they believed it was flat.