Romans had a signifier for every century, and we see on films or shows armies with many cool flags. Would real medieval armies have such?
By all means yes. Given that the system of feudal relations developing in early-to-high Middle Ages resulted in quite the dispersion of power, especially in continental Europe, the troops were usually marshaled on gradual basis, meaning that if, say, a suzerain was going to war, he was calling upon the nobles answering directly to him, these were calling their vassals obliged to support their seniors with military service, and so on. To keep things organized, the troops were organized in units that in some countries were literally called a 'banner' because their position on battlefield was marked by the specific banner carried by a standard-bearer (that served both as the visual signal for the commander and a rally point for the combatants). A single 'banner' (or company) usually consisted of the knights hailing from a specific region (land banner) or of vassals of a single powerful noble (house banner) and could have counted anything between 40 and 100 knights. It should be noted however, that the actual number off combatants in such unit was several times higher, as each knight was usually obliged to arrive with his retinue (lance, lance-fournie), usually consisting of several combatants, armed and equipped as per agreement with his senior, the most common composition being the knight himself, one or two similarly armed companions (often squires) and several lightly armed supporters protecting their master from the back. Later, with the emergence of professional armies, the flags and banners of the respective units largely remained, serving the same purpose.
As each company consisting of few hundred combatants and was indicated by a separate flag, one can easily imagine that there had to be quite a few banners on each side of the pitched medieval battle. And this would be quite correct impression. For example, in the Battle of Tannenberg in 1410, the forces of the Polish-Lithuanian side numbered 28.000 people divided into over 90 separate companies, not counting Czech, Moravian and Mongol companies, while the Teutonic Order and their allies fielded 21.000 people divided into at least 52 companies. This, of course, was one of the biggest medieval battles but other battles fought in the late Middle Ages tended to fall into this order of magnitude. On a side note, most of the banners of the Teutonic companies were collected after the battle and their images were collected in the book 'Banderia Prutenorum' (Flags of the Prussians) depicting 56 flags used by the Order and their allies (both the banners of the respective companies and personal flags used by the Order, the Grandmaster and other high-ranking Order officials).