Straight Bladed, Double Edged Blades
Most common in my campaign are the straight-bladed two-edged weapons. These typically are suited for both cutting and thrusting. Common materials are bronze, iron, and steel.
Dagger: think "almost sword." This is a heavy weapon along the lines of the Bowie knife. The blade is shorter than 16" and both single- and double-edged types are commonly encountered.
Short Sword: has a blade varying between 1.5' and 2' in length.
Long Sword: has a blade from 2' to 3.5' in length and is the longest blade intended exclusively for wielding one-handed.
Broad Sword: approximately the same length has a long sword but with a wider blade and less pronounced point. Broad swords are intended mainly for cutting attacks.
Bastard Swords: has a four foot blade and longer hilt. This weapon can be used either one- or two-handed.
Two-Handed Sword: a long bladed weapon, together with hilt the weapon is about 6' long. Intended for wielding with both hands. While it can both cut and thrust, it is primarily a cutting weapon.
Straight Bladed, Single Edged Weapons
Falchion: this is a cutting weapon that looks a bit like the modern machete. Similar examples include the Chinese dao and the Persian shamshir. Falchions are popular among mercenaries and as a result the weapon has acquired a bit of low reputation among the highborn.
Backsword: has a long single-edged blade with point. The backsword could be used for both cutting and thrusting. Cheaper than a longsword and, like the falchion, is popular with sellswords.
Curve Bladed, Single Edged Weapons
Scimitar: the most easily called to mind example. The scimitar is primarily a slashing/cutting weapon and has many variants in Earth cultures. Examples include the Turkish kilij and the Indian talwar. Scimitars and variants of the scimitar are popular weapons among the humanoids.
Khopesh: the Egyptian sickle sword that probably evolved from the battle-axe.
Kopis: a heavy knife or short sword with a forward curving blade.
Kukri: similar to the kopis but with a much shorter blade.