I'm not very knowledgeable about the Medieval time period, so let's just go by whenever the "peak" of the medieval period was. To expand, I've seen posts on here about the weak points knights would exploit in each others armor as well as tactics and equipments they would use to defeat each other, but my question is how would a normal levy soldier fair? Would he have the training and equipment to put up a fight or would the knight essentially run over him? While we're at it, where would mercenaries stand? Surely they would have similar combat experience, could a seasoned veteran give a knight a run for his money? I understand battles were pretty much always formation based and didn't allow for the duels you always see in movies, but let's just pretend somehow the knight comes face to face with one of these guys on foot.
Let's take a Western European night or man at arms from the late 13th century as an example.
His armament and training would be significantly better than a common conscript-
A horse: This is a significant advantage, but still prior to the widespread development of anti-cavalry tactics like schiltroms and pike formations. Ultimately the late 14th century and 15th century found the focus shift to unmounted heavy troops.
Armor- At this time the common armor would be mail maybe with supplemental material (steel plating or leather). This would have been significantly more protective than the padded jacks or leather of common infantry (if they had any armor over a helmet at all).
Weapons- At this time the Knight's lance and horse was still dominant on the battlefield. They would have access to the exact tools suited for their jobs.
Training, Knights and men-at-arms were professional soldiers. They trained for years to fight in wars. This is a HUGE advantage over a peasant who might have some brawling experience. More than that, a professional soldier would know how to think tactically in the battle and avoid situations that put him at a disadvantage.
Also, the knight would be considerably more fit than a peasant, especially for battle. Knights trained daily, were well fed, and most importantly- did exercises directed at preparing for battle. While a common farmer may be very strong, they would not have developed their muscles to effectively wield a poleax or sword.
Tldr- Take a common person on the street and give him a hunting rifle. Put him in a field and have him fight an army ranger with full gear. Chances are about the same.
While we're at it, where would mercenaries stand? Surely they would have similar combat experience, could a seasoned veteran give a knight a run for his money?
Absolutely, there was nothing inherently special about a knight over a man-at-arms or a battle-hardened mercenary. The knight might have access to better training, but the skill levels would even out quickly when we start talking about heavily armed professional soldiers.
I'd also point out that while professional heavy cavalry outclassed common infantry, that did not make them invincible. Tactical blunders during a battle could get the knights bogged down, which eliminated their advantages and made them vulnerable. Famous examples include many of the English victories in the hundred years war (Crecy, Agincourt).
For descriptions of military equipment and armies see "Arms and Armor of the Crusading Era" by David Nicolle, and I'm sure there are many others.
Terrain is also an important factor. In his general history of the Netherlands*, Han van der Horst mentions multiple instances of knights getting stuck in a swamp with their heavy armour, and promptly getting massacred by untrained, poorly-armed peasant militias.
* Nederland: de vaderlandse geschiedenis van de prehistorie tot nu. First published 2000, many updated editions since.
This is an interesting question I was actually going to ask (Sorry for piggybacking)
How would a normal levy soldier fare against a Knight during the High Middle Ages? Let's say around 1066?
What is very important for this question is around which age you mean. 14th or 11th century really makes a difference in the answer.
Adding to the answers, it's important to distinguish between 1v1 fight and group vs group fight. In the former, your average levy soldier is at a tremendous disadvantage. The knight may have a horse (although many often fight dismounted), a superior weapon, and an armor that gives significant protection against the levy's weapon.
All that said, when a group of knights fight a group of levy soldiers, the dynamic is changed significantly. A disciplined group of spearman can challenge a mounted knight, or even a group of mounted knights. It depends on the terrain and the setting, of course, but it's not nearly the same significant disadvantage as in the 1v1 scenario.
When the longbow is mentioned, it is important to view that in the context of an engagement between a group of longbowmen and a group of knights. In a 1v1 fight, the longbowman cannot win lest with significant luck.
All this is to set the stage for what comes later, namely the introduction of the pike formation, and later the introduction of firearms. A pike formation of disciplined soldiers is very tough to beat. And firearms give the common soldier a strong punch at lower and lower costs as both technology and infrastructure improved.