In popular culture it seems it that the threat of armed was ever present to people travelling around this time, I'm interested to know to what degree this was a reality. Additionally how well armed would such people have been in the late middle ages and early modern era (for the purposes of this question 1400-1600 ad)
It really depends on the time and place. I will talk about England and France in the Late Middle Ages a bit. In England, violence in the shires would increase during times of political unrest (deposition of Edward II or Richard II, weak rule of Henry IV and Henry VI) and was always more prevalent on the Welsh and Scottish marches. The Scottish march especially suffered from constant raids and counter raids from one side of the border to the other and general impoverishment which made people turn to violence to support themselves. In general in England brigandage would ebb and flow, and from what I have read rarely came to such a level as utterly destroying the fabric of society or government outside of the border regions.
France is an entirely different matter. Bands of routiers -- autonomous companies of soldiers who fought for themselves rather than a sovereign -- would spring up during certain periods of the war when the French government collapsed (1350s-1360s, civil wars of the early 15th century) and were also almost always present on the Gascon march in Southwestern France. The boundary between private and public war was quite blurred in this period so it was easy for the routiers to claim that they were fighting for a prince (usually the King of England, in later periods also the Armagnacs/Dauphin or the Duke of Burgundy) while actually serving themselves. Rather than simply roaming the roads to steal, routier companies would seize a fortress (a castle of some sort, sometimes a fortified abbey or manor house) and raid the country around it using the fortress as a base. They would steal and murder, but also demand patis or protection money from the surrounding area for not causing more destruction. During the climaxes of the Hundred Years War -- such as what I mentioned before, the period between 1356 when John II was captured at the Battle of Poitiers and the late 1360s when the French government reestablished itself on sure footing under Charles V, and the Armagnac-Burgundian civil war that began in 1411 and led to the English invasion of 1415 -- routier activity largely destroyed functioning government in much of France and led to widespread chaos and destruction. This was very persistent in certain regions like the Gascon march which almost always suffered from routier activity (there garrisons were even allowed to remain during periods of peace/truce like between the 1390s and 1415) and in Lancastrian Normandy or the march of Burgundy in the later part of the war.
Also it is important to note that the phenomena described above were not unique to France or the Middle Ages, and occurred during major "Early Modern" (I hate that term it's meaningless) wars such as the French Wars of Religion or the 30 Years War -- where public wars created the conditions for a breakdown of order and the abandonment of the countryside to raiders. The bandits/brigands/routier were usually professional soldiers who stopped fighting for their monarch in order to enrich themselves, and the companies would usually draw other men from the lowest rungs of society (criminals and impoverished city and country dwellers) to reenforce their numbers.
Sources:
If I may add a question, who exactly were these bandits? Were they demobilised soldiers (brigands) or something else?
I'd like to add a further question of what reliable sources exist that are readily accessible through standard means (bookstores, internet, libraries, etc) that document banditry in the middle centuries of the first millennium ad