In the 13th Age roleplaying game, if you’re fighting an enemy with a sword, axe, spear or other melee weapon, according to the rules the two of you are engaged. (Congratulations!)*
If one of you wants to break off the fight and go somewhere else — whether to retreat, or to run over and help your buddy, or attack someone else — you have to roll a disengage check on a 20-sided die. A successful roll means you break off combat and move away with no penalty. A failed roll gives you two options. You can stay in combat (with no penalty), or you can disengage anyway, and your enemy gets a free swing at you. This, for those unfamiliar with roleplaying games, is called an “opportunity attack” or “attack of opportunity.”
On an RPGnet thread about 13th Age, someone who hadn’t yet seen the game said that opportunity attacks in the rules were a deal-breaker for him. This prompted someone else to ask how long this rule has been around in D&D. This sort of question puts me into Obsessive Researcher Mode.
I pulled out my Moldvay Basic and 1st edition Advanced Dungeons & Dragons books, and went hunting. Sure enough, early versions of opportunity attacks were there under different names.
In Moldvay D&D Basic (1981), page B25 describes two ways of breaking off engagement in melee combat. In a “fighting withdrawal” the defender can back up at half his movement rate without becoming vulnerable. A retreat allows the defender to move backward at more than 1/2 movement, but gives his opponent +2 to hit and the defender can’t make return attacks.
The 1st edition Dungeon Masters Guide
So opportunity attacks go back to at least 1e. If you own 0E or Holmes Basic, I’d love to know if it’s in there as well.
*That joke never gets old.
Wade Rockett 
From Holmes Basic (July 1977), pg 20:
“If combat is broken off, the fleeing party must accept an attack without any return on his part, the attacker adding +2 to his die roll for hit probability, and the armor class of the fleeing party can not include a shield”
and
“A character in melee may withdraw from combat if there is space beside or behind him to withdraw into. His opponent gets a free swing at him as he does so with an attacker bonus of +2 on the die roll, and shields do not count as protection when withdrawing”
and
“If an opposing figure is killed or withdraws, the attacker may advance or pursue immediately — if the player desires — or he may take some other action.”
In Dave’s early Blackmoor games (72-74), he awarded “free chops” in these types of situations. So attacks of opportunity actually pre-date D&D.