In Inquisitor, a spin off of Warhammer 40,000, you can choose to aim for an opponent's groin. It causes a fair bit of damage, and leaves them almost useless for a turn. Not to mention, it's goddamn funny.
Some players have remarked about unusually accurate shots from meltaguns ("weaponised microwave oven" is a fairly accurate description) and chainswords.
In the Ork Codex, a mortally-wounded Warboss did this to a Bloodthirster as a kind of "parting shot". With a Power Klaw.
I.C.E.'s Cyber World had the following entry in the "Critical Failure: Melee" table: "Worst move seen in years. You take 60 pts of damage to your own groin. Opponent stunned for 3 rounds with laughter."
In Warhammer Fantasy Roleplay the Bretonian truffle hound is noted as becoming extremely jealous of any males in the vicinity after eating a truffle, and will take steps to rectify the situation. The consequences are not spelled out, but are still pretty obvious.
In GURPS this is very effective, causing twice the normal shock penalty.
If you're small enough the game allows you to upper-cut an enemy in the groin.
There's also the "Testicle Grab" technique.
If you randomly attack someone the groin is the second most likely part of the body to be hit.
Werewolf The Apocalypse has one entry on the Battle Scars table labeled simply "Ahem..." The injured spot isn't named, but it's specified that you are now immune to seduction attempts, unable to seduce others, and (if male) sterile.
In Hackmaster, gnome titans have a special "groin stomp" attack, and characters can perform a "groin punch" attack.
The Celestial Monkey martial arts style in Exalted lets you make a called shot to an opponent's primary virtues, as represented by areas of the body. In Valour's case, said area is the groin (something of a pun on "balls of steel"). This does up to five levels of lethal damage depending on the enemy's courage, which is impressive considering that just-starting Exalts and heroic mortals only have seven. (You can punch a moderately-brave extra in the crotch so hard he dies. Never let it be said that Exalted does anything by halves.)
It should be noted that this is bonus damage in addition to whatever damage got past their soak, making it possible kill an Exalt with a kick to the nuts.
Perhaps showing The Monster Squad as one of its influences, Grimm has an advantage that can be taken by PCs who already have the advantage "Dirty Fighting" called "Right In The Nards!", and the rules on combat feature an illustration of a kid kicking a wolf-man in the crotch.
The fan created netbook "Guide To Unlawful Carnal Knowledge" for AD&D features "The Rack Critical Hit Table," which basically shows the various results of a male character getting "racked."
Played for Drama
Seth Farrow, recurring villain in Scion, took a shotgun blast to the groin the night he murdered his nephew Horace's family. It's never stated outright, but it's clearly implied he lost his genitals; most notably, when a captured Donnie Rhodes greets him with "How they hangin'?", Seth pulls a knife on him (Kane barely keeps him from using it).
Iron Crown Enterprises: Any location based damage in HARP or Rolemaster with a hit location of "Abdomen and Groin".
