In Super Swing Golf Pang Ya, lower-tier opponents will make the most blatantly idiotic shots.
A discussion of the AI stupidity in Madden NFL would take all night, but one that deserves mention is that the AI has serious trouble with quarterbacks doing rollouts. If the AI is tasked with guarding the receiver and the QB rolls to his side, the AI defender will often come up to play the QB and then get indecisive, leaving both the pass and the run wide open.
In Backyard Baseball, if there is a person on third base, the fielders automatically throw to home. Usually it is an outfielder that does this, and almost always a run is still scored.
For some reason the AI in FIFA 2000 (and its spin-off, The FA Premier League Stars) was totally incapable of dealing with set-pieces correctly. This meant that whenever you got a free kick, half of the time the computer team didn't even bother setting up the wall, and when it did the wall tended to be completely out of position. Corner-kicks were even worse, as your own players weren't marked correctly and the opposing goalkeeper was far too slow to react, meaning that so long that you were able to get plenty of corners, you could ratchet up huge scorelines even on the hardest difficulty settings.
Invoked in FIFA 95 with the Stupid Team Cheat. Any team this was used on turned into the biggest bunch of halfwits ever to grace a football pitch. Most amusingly, goalkeepers would drop saved shots between their legs, allowing a player to tackle them to score a goal.
Mario Basketball 3-on-3. You control one character at a time. Your two teammates do nothing while you desparately try to avoid getting the ball stolen. The ball falls right next to them? They still do nothing.
In Pro Cycling Manager 2011, when a breakaway occurs, a team start chasing a group containing their own riders like it was one of their worst rivals. Pack takes them back in. New breakaway, some different riders, one from before mentioned team is in. Same team takes up the chase and wins. New breakaway, same teams, minus the one chasing before takes part. The team chasing before has stopped, because they weren't destroying it for their own team anymore.
In Pro Cycling Manager 2014, and previous editions, the AI has a tendency to gang up on the player, refusing to do work whatsoever, even when it logically should. As an example, in real life, during a cobbled classic, if someone's on the break at the end, everyone takes part in the chasing the person down, because they want to win. In the game, the AI leaves the chasing to the player controlled rider, and decides to just suck wheel, even if there's a very slim chance that the player controlled rider will ever chase down the guy on the break, and by that reducing their own winning chances to nearly zero - a chance that real cyclists would never take.
Tiger Woods PGA Tour 2006 gives excellent examples of this. The AI has a habit of making really poor shots (and almost always being unable to make a putt longer than 5 feet). This would range from always hitting the ball into the bunker to hitting the ball out of bounds. The December 11 event in RTE mode plays this Up to Eleven, when the opponent team consisting of Jon Hozzle and John Dinkenbach, often makes really poor shots to the point of hilarity. The scores would range between Bogey to 5 over Par per hole. Your partner, Danny Wheeler, also falls victim to this, even if it is to a lesser extent. Even the PGA pros and legends can't avoid this trope, as the likes of Justin Rose and Arnold Palmer can hit the ball into the water hazard at times. It is because of this trope that some players of the game criticise it for not providing enough challenge.