The Command & Conquer games alone have many examples of this, most evident in the first game, Tiberian Dawn. Some of the Aritificial Stupidities may overlap each other.
Tiberian Dawn has the most of them all and are is easiest to exploit. Some examples follow:
Wall Ignorance — The AI would not target walls even if they were built into its base. This means you can literally build a chain of cheap sandbags right into its base, build armed buildings there and block all the exits with walls so that their units can't get out.
Suicidal Overconfidence — The AI has a knack of fixating the first enemy it encounters until that enemy's defeated. This leads to almost total ignorance of anything else on the field, and will result in the AI sending loads and loads of units on suicidal runs against heavily fortified positions again and again until it runs out of resources.
When the AI sends all it's units into attack mode, the Harvesters attempt to attack, too. While this makes sense in RA 2 where half the harvesters have mounted machine guns, that's several years down the line.
Blind Shortcutting — When given a command (by a commanding player or by the game's internal mechanics) units will use shortest route possible, even if it means running into a trap of a thousand guns. And if they're shot, they don't fire back, either. This is can be either a nuisance or an exploitable flaw, depending on whether you're losing or winning. See this video (starting from 6:40) for a hilarious, satirical parody of this loophole, complete with Double Take, for a demonstration.
Also, the shortest distance is determined with algebra, not calculus; that is, it takes the distance from point A to point B, ignoring any obstacles, meaning a slightly farther tiberium patch will be ignored despite having to go much further to get to the "closer" one.
If the player has two Harvesters, one attempting to return to base and the other to go out and collect through the same narrow path, the units will sometimes meet, turn twice (each time continuing to block the other's progress)... And then center their orientation, and move right through each other... The last few seconds of the clip above demonstrates this.
Blind Harvester Replacement — An easy way to defeat the AI is to make them broke. To do that, you have to kill the AI's Harvesters which the AI will insist on replacing until runs out of credits to replace them... or, for that matter, anything else in its arsenal. At this point, the AI becomes a pushover and is wide open to attack.
If you side with Nod, you can take a Recon Bike and attack an enemy Harvester without losses. The Harvester is programmed to cease harvesting and attempt to run the Bike over as though it was a crushable infantryman, but since the Bike is a vehicle instead, it will fail to run the Bike over and just stand in front of the Bike like a sitting duck. It will remain fixated to the Bike and following the Bike everywhere, even if it means driving into a trap.
This might have been changed with a specific patch, but at least in some versions of the game it was perfectly possible to run over a bike with a harvester.
If you side with GDI you can do this by attacking the Harvester with a Rocket Soldier and then ordering that Rocket Soldier to escape back to base in an APC.
Targeting Fixation — As Nod, you could completely avoid GDI air strikes by leaving an infantryman in the north-east corner of the map. The AI would always target this one man instead of your army or base.
In general, the AI in Command & Conquer is purely scripted and doe not respont to the type, number or direction you attack it at all. Each map data tell the AI when to build which units, and which way they should take to your base. This explains why the exact same enemy unit compositions attack after specific time intervalls again and again, and why they keep getting blocked by simple sandbag walls.
Red Alert examples:
Pathfinding Stupidity — The AI would often decide that sending units as far as possible toward the north-western corner of the map, regardless of if there were enemy forces present, was an absolute priority. Cue a large multicoloured mass of AI units all moving to this one corner, ignoring each other completely in the process. This is most commonly seen in the V3.03 patch, but is also known to occur in all other versions.
The AI has a hopeless strategy in Skirmish games - it will typically build a base and send a single large attack at the player, after which it will cease most operation. The AI also builds its bases in a manner that contributes to the problem by making passages between buildings small and often crowded with infantry.
Red Alert 2 examples:
Targeting Fixation — When using superweapons, the AI suffers a similar problem to the one encountered Tiberian Dawn, only it was based on buildings. The AI would always target any super weapons you had, then any war factories, then your naval yards. And it would be the most recently built one as well. So all you had to do to avoid superweapons was place a targeted building away from the base.
When you play against hard computer with superweapons, just build a warfactory right beside their base right when their superweapon is ready, they'll be stupid enough to nuke themselves. And sell the building as soon as the superweapon is launched
The Allied (As opposed to Soviet, not allied as in allied with the player) AI will also fixate when it comes to using its jets. It will always attack the first tank built until it is destroyed. You can exploit this by putting that tank at the back of your base behind heavy anti-air and the AI will keep wasting its jets over and over again.
Suicidal Overconfidence — Unless there's an enemy unit nearby, the pathfinder would always take the exact same path to the enemy base. This led to situations where the player could amass a gigantic wall of artillery pieces and have them auto-target a single small area in which all enemy units passed through, and enemy units would always blindly go through the massive killzone, never changing up their pathfinding at all.
Considering playing the Nuclear General in the Zero Hour expansion, upgrade to Neutron Bombs and have 4 Neutron Artillery cannons force-fire on the path the AI takes. Every five minutes or so, scoop up the empty vehicles with your own infantry. Instant tank army at a very low cost!
Generals (and ZH) has prelaid AI pathwork, if you look in the map editor. So this explains it. Made the SP/skirmish game far too easy if you knew the AI paths (or looked em up using the handy map editor included with the game!).
In Generals (without the Expansion Pack) the USA AI had very poor strategy (bear with the Unfortunate Implications). With their units thrown erratically at your base, they almost refused to build defenses, and could be defeated just because they went bankrupt from their stupidity.
The higher-difficulty USA AIs in Zero Hour also make a mistake that the lower-ones don't. The brutal AI doesn't seem to grasp the fact that the Avenger's an anti-air unit, and its anti-ground attack is a targetting laser that doesn't do any damage whatsoever.
Tiberium Wars examples:
Stone Walling — A base can become invincible against the AI with a good mixture of all usable kinds of turrets and aircraft for base defense. Then, after wearing the enemy's ability to attack, send in the aircraft to do bombing missions while selling off the turrets in place of more aircraft.
Suicidal Overconfidence — The AI generally wasn't the brightest of the bunch. As a result, your rare allies would barely ever follow you to the area after the one you met them in, given that they survived against the respawning enemies while you killed the Officers (thus disabling respawns). The only allies that were able to follow you were Escort Mission targets, which in turn had the tendency to stand between you and the enemies. They also didn't follow you as much as mindlessly charging ahead after you caught up with them at a checkpoint or saved them from enemies.