Weapons of the medieval ages evolved with the change of armor (my observation), but was also propelled by the invention and improvement of ballistics. A large list of medieval weapons and their description can be found here

 

There are many different kinds of melee weapons. They are classified by the way they kill, and how they are mounted

 

Polearms

Polearms are generally cutting or impaling blades/points mounted on a long staff. An example of this is the halberd, multipurpose impaling/cutting weapon. The halberd has an axehead mounted on a long staff that one can swing. Also, variations of this weapon are called the poleaxe. A spear may be counted as a polearm

 

Blades

Blades are usually mounted with a handle, long or short, used for thrusting, or cutting. Blade weapons come as single wield and two-handed wield weapons. Much attention was focused on training warriors specialized in these weapons for they were versatile and easy to handle. From daggers to great swords, or two-handed swords, blades are perhaps the most diverse class of weapons (maybe matched only by clubs, man's oldest weapon ;-) )

 

Axes/Maces/Hammers

As armor became thicker and thicker, swords were found to be ineffective against tough steel. Axes struck hard and pierced armor fairly easily. Spiked or flanged maces were often used to crush bones and armor. War-Hammers were perhaps one of the most fearful of them all, large with a heavy head, capable of knocking out or killing a knight inside his armor with one blow.

 

Clubs, etc

These were used in various forms by various groups of people. Often, the weapon was upgraded into a form of mace or flail. Flails were fairly large handles attached to a head by a chain. The heads were sometimes spiked, and sometimes just heavy weights that were used to strike, crush, or pierce an opponent's armor.

 

Ballistics

As missile weapons grew in power and accuracy, armor was rendered useless. The crossbow could pierce thick plate with a heavy bolt. Longbows at close range were quite deadly, and could be shot at an alarmingly fast rate. The catapult, ballista, trebuchet, and most importantly, the cannon ended the feudal era and period of history, as cannons destroyed the protection castle walls previously gave to peasants. These peasants in turn, had no reason to work for their local warlord, and the feudal system failed.