In earlier editions of D&D, such as 3.5, a character could throw a melee weapon using feats like Throw Anything.
In D&D 5th edition, is there any rule, ability, or method which would allow a player character to throw a one-handed melee weapon without the Thrown property, such as a longsword?
The relevant excerpt from the Improvised Weapon rules in the Player's Handbook (p.148):
So any weapon can be thrown, however they will deal significantly less damage. This can be done without any special training. Taking the Tavern Brawler feat (PHB p. 170) will grant you proficiency in the relevant attack.