Big Rigs: Over the Road Racing's opponent AI...or complete lack thereof, seeing as the opponent just sits there; you can't even push it to its victory since you'll just clip through. If there is an AI, it stops short of the finish line. You literally cannotlose.
In 3, AI drivers will occasionally spontaneously swerve all over the road and mash into each other, and it's easy for them to get stuck on each other. They also did not have upgraded cars, turning single player "races" into glorified hotlapping. Forza 4 improves the AI greatly and makes the AI drive upgraded cars, but the AI will still abruptly swerve for the racing line when the player leaves Rewind.
In Forza 4, Track Day (hotlapping while AI cars simulate slower traffic) events in Rivals. Tha AI are painfully slow, reaching single digits in some corners, and they will regularly pull out into your path, sometimes for no reason at all. This turns the longer events into Those Two Levels.
Sometimes, when AI are in use in online races on Forza 4, an AI car will lose a lot of speed due to leaving the track or being involved in a crash and go into ghost mode. Another AI car will then slow down behind it, driving inside the ghosted AI car and causing them to both come to a stop to try to avoid crashing into each other, effectively indefinitely removing them from the race.
Occasionally if you hit the rewind feature and then resume the race immediately, the AI drivers either won't realise the rewind has occurred and continue driving from where they left off (often crashing into a barrier, or one another, or even you), or will wildly over-compensate (again plunging head-long into the closest barrier).
In Forza 5, the AI has no concept of re-entering the track safely after shooting wide on a corner or an incident and will happily swerve right into a fresh incident.
When presented with a y-junction or off-ramp, the civilian cars in Test Drive 6 will indecisively swerve left and right until they ultimately crash into the divider. Every car. Every time. If you don't pass civilian cars consistently and efficiently, you'll get caught behind an unprovoked 30+ car pileup.
The AI cars in many racing games, especially the Gran Turismo series, tend to follow a set pattern. Even in the most recent installment that was in Development Hell for five years. Also, in the B-Spec game mode, you take a role as an AI's director on a race. The problem is, your AI can't pull off the car's full potential. Even if you do well on directing the driver, the result of the race can still be bad because the AI is terrible at pressure control and slipstream.
In Need for Speed Shift 2: Unleashed, your opponents make no attempt to avoid you if you make a mistake and get in their way. This almost always results in you facing the wrong way and watching everyone pass you or worse, wrecking your car.
In Destruction Derby 2, there was a track where the road narrows just after the start. Stop here, or spin out an opponent, and everyone would jam in there and get stuck, leaving you free to cruise away. Even if they finally got out, you were almost a lap ahead at that point.
Carmageddon. The battles took place on a number of large maps with easily avoidable barriers placed depending on which race you picked for the few people who actually wanted to drive laps instead of going into the city and killing everyone. The problem: the AI didn't get the memo about those barriers. Only Offscreen Teleportation saved the AI from inevitably getting stuck on them and never moving again for the entire fight.
The CPU characters in Mario Kart are pretty stupid, except when you're in first place and they suddenly decide to make all the perfect moves (and one of them always has a blue shell). An example is Mario Kart 64, where the computers will often throw banana peels hoping for you to go on them, only to later slip on them themselves, though they will still be able to catch up with you, thanks to the Rubber Band AI. Playing Team VS or Team Battle with the AI is an aneurysm waiting to happen. When the AI is on your side, they actively work to make you lose, such as not being aggressive against the enemy AI or dropping their defenses to let themselves be hit by attacks. When the AI is against you, they are the classic Mario Kart AI.
Wipeout. Autopilot power-up. Ranges from magically good (XL, Wip3out where it would fly through the track boundary walls to keep you on course) to virtually useless (Fusion, where using it in any slightly difficult turn would cause it to plow repeatedly into things and finally turn around and leave you going the wrong way and headed at top speed for a ravine). Pulse was halfway between the two, usually managing to find its way around the course but at such an incredibly slow speed that it was virtually useless. One constant, though, has been the fact that if there are mines in your way, it will always go right through them, because it follows the same path as the AI ships that dropped the mines.
Midtown Madness 3 has some the dumbest cops ever. Drive into a body of water while the cop cars are chasing you in cruise, the cops will follow you. Then, they will respawn right near the water and drive into it again and again and again, even when you drive away from the water when you respawn.
In the battle mode in Diddy Kong Racing, AI characters have set move patterns, making them easy to defeat once you've figured out the direction in which they'll go.
The same can be said about Crash Team Racing. The AI cars rigidly follow a set path like trains, allowing you to win every race with ease. It can actually be pretty funny watching the same car get eaten by the same monster plant EVERY SINGLE LAP it takes in the Papu's Pyramid stage. The bosses take it a step further, and roar down the dead center of the racetrack. Knowing this, the boss battles become unbelievably easy even though they have all-around better stats and can spam weapons infinitely. Papu Papu cranks this Up to Eleven. The stage you race him in conveniently has a line going down the dead center of the track which he follows religiously for the entire race. By placing every potion and nitro crate you get on the line, he'll never pass you once.
Prior to version 0.8, AI karts liked to follow a set path, even if this path goes around bonuses or into obstacles. They were often too stupid to dodge a bubblegum on center of track.
A bunch of AI karts may aim for the item box on the left, leaving open the item box on the right.
In rare moments, an AI kart will boost at the wrong time, and launch itself off the track.
The AI can't handle certain curves. Some examples include, Blackhill Mansion in Reverse Mode, and the Minigolf track.
A rare occurrence, an AI kart can get stuck in a literal wall banger. A stuck AI will usually hit its own Reset Button, but not if the kart is bouncing off a wall in front. If a kart is far behind everyone, this is probably what happened. A good place to observe this is XR591 in "Follow the Leader" mode. If the leader gets stuck, everyone else will try to stay behind the leader.
Iggy's Reckin' Balls: The AI can occasionally get stuck in a loop trying to make a jump that it cannot make, or repeatedly missing the timing on a moving platform. It also tends to have problems making consecutive Drop-Swing Jumps, which paradoxically make some of the more advanced courses easier to win (as the Drop-Swing is a tricky maneuver that mostly shows up in advanced races).
At low levels, the CPU in Supra Mayro Kratt will race at the very slowest for no reason. Intentional on the part of the developers, as this game is Stylistic Suck incarnate.
The original Formula One on Sony PlayStation featured a glorious AI error where the AI cars would pit on every single lap following their first pitstop in longer races. Additionally, the sequel Formula One '97 had a glitch on one of the Bonus Circuits where Jean Alesi and Gerhard Berger were faster than anyone else. This would normally be a bad thing, but they also stuck to the racing line like glue which meant that they would constantly damage their front wing by hitting every car they came up against. Cue tons of AI cars (and yourself) pitting every other lap for repairs should a Bennetton catch up with them.