In Runescape, the enemies will attempt to follow a straight line to their target (i.e. you), so it is often possible to stop them in their tracks simply by hiding behind something, even a torch. This may be deliberate, as the only practical method for archers to level up is to get a target on the other side of a table, fence, or similar obstacle, and proceed to turn the target into a pincushion.
Mages can use the same strategy. Also, your character can also get stuck behind stuff, since you walk by clicking on where you want to go. In other words, you can also get this problem, though the player can guide their character.
In Guild Wars, one of the quests involves a 1 on 1 fight against an Evil Twin who is modestly stronger than you, and has the exact same skills on his skill bar that you do. The primary (and intended) way to beat him is to invoke his Artificial Stupidity by taking skills useless for a duel, and/or by taking good skills that he will not actually use. For example, it's entirely possible to get the Evil Twin to sacrifice enough of its health that you need only give him a cherry tap to win.
The Artificial Stupidity of henchmen in Guild Wars is acknowledged in the endgame area of Prophecies, where Reyna reminisces how she often would use her single-use resurrection, not on a player, but instead on another henchman who would ultimately die trying to resurrect other henchmen.
It's actually an established tactic as Squishy Wizard to go for cover, because spells from skills can bypass objects but weapon damage cannot. While the pure melee Non Player Characters indeed have a working pathfinding, all others will nuke the wall ad infinitum and can be picked off one by one. Of course, the same goes for your henchmen and minions—with the latter ones being especially frustrating because you cannot order them to stop.
City of Heroes' enemy AI is usually pretty good, but some of the NPC allies you get on certain missions are appallingly dumb. Fusionette, a recurring NPC, does an unfortunately good imitation of a novice player with her tendency to attack too many enemies at once and get clobbered.
And in City of Villains, on the timed "Mayhem Missions", it's often possible to spring a NPC villain from jail for a little extra firepower against the hordes of police and heroes trying to stop you. Which is fine, except they often have an annoying glitch where they stand in front of some easily-destroyed object without attacking. No wonder they were arrested so easily...
Even worse (this is less of an issue with player pets than NPC villains, simply because they're replaceable), if you've been smashing things they tend to get in on the action, which might be good... except that they don't understand the concept of "explodes upon destruction". They can knock themselves out with no enemies in sight.
Mastermind pets are incredibly stupid as well. For example, if an enemy NPC tries to flee, your pets will chase after it. Once that mob is dead, they will come running back to you. All the while completely oblivious to half the map's enemy NPCs chasing and shooting at them.
In La Tale enemies will follow and attack the first player character they see, regardless of threat level or feasibility of actually doing damage. They will ignore anyone else unless they don't get a chance to attack for at least a minute or the character moves out of range. This can be abused while in a party to kill vastly more powerful monsters than you would normally stand a chance against by having one character act as bait, run like hell, and climb a ladder just out of range. The rest of the party can attack the monster with impunity until it finally gets bored and goes after someone else. Rinse and repeat and you can defeat even mobs of high-threat enemies with little risk.
World of Warcraft has two types of situations where your character is 'used' by the computer: either when fighting/aiding a doppleganger, or when mindcontrolled by certain bosses. Dopplegangers will sometimes use abilities with no cast time, but will almost always fight in melee range and spend most of the time just hitting with their melee weapon. Still a little threatening if the copied player is a Rogue, not so effective if they're a Mage whacking away with their staff. For the latter situation, while mindcontrolled your character uses abilities almost constantly and somewhat randomly, and often makes interesting choices (for instance an AI controlled Paladin using nothing but 'Exorcism' - a mediocre damage spell that usually only works on demons and undead - over and over on a fellow player). One particularly weird case showed the mind-controlled character apparently deciding Screw This, I'm Outta Here, and using a spell to teleport themselves to a different dimension. One constant is that they tend to use all cooldown abilities. Which due to their other actions is not necessarily dangerous, but does deprive you of them.
Particularly amusing is when the boss makes the player's character use an ability that breaks the mind control. The same ability that the player would use in that situation if they had control of their character.
At least some enemies capable of mind control seem to have a keen interest in Archaeology (or else are very curious about what all the buttons do), as they will often make the mind-controlled character use the "Survey" ability. Not only does survey have a cast time, but is also not a combat ability in any way, shape or form.
Dungeons & Dragons Online allows you to use computer-controlled hirelings that have a tendency to charge off into the distance on their own to attack bad guys. Bad enough, except they tend to run through deadly traps on the way. Or just stupidly stand IN the traps until dead. Particularly annoying when hireling clerics (healers) just stand in the trap attempting to heal themselves rather than move out the way first (and the traps deal way more damage per second than the healing so they just die anyway).
Hirelings in Diablo clearly fall into this trope. While the enemy AI is okay, the ally AI is definitely not. Hirelings don't seem to understand basic concepts like "I should use that door just a few steps from me instead of trying to walk through the wall", they have the annoying habit of exploring all the whole time in a world where just walking a few metres triggers a new wave of dozens of enemies... And monsters by the Necromancer are even worse, as getting too far from them (and they aren't good AT ALL at following you) makes them disappear. After numerous reports of necromancers getting stuck in a corner by their minions, Blizzard added an Unsummon skill to remove them when needed.
Puppetmasters in Final Fantasy XI Online will often run afoul of this trope. Their automatons can be configured for various roles, two of which are the Soulsoother and the Spiritreaver.
Soulsoother will cure status afflictions and heal, in that specific order, which means that it will always remove that weak Poison or Silence (which has no effect on a non-casting job) instead of a 900 HP cure when the player is near death. This same automaton also has an ability to deal damage based on the amount of damage it received, yet any damage worth mentioning is almost always healed by it prior to using said ability with an overkill heal... (unless its cast timer is down at that moment)
Spiritreaver will mainly cast highly damaging spells, and it attempts to do so intelligently: it can determine up front if a spell will land, and choose a more effective spell if not.. 'effective' being the ability to land a spell unresisted, not the amount of damage dealt. That the target cuts magic damage by 90%, or even absorbs magic damage and gets healed by it, is ignored. When this automaton gets below 75% of maximum MP (due to casting those damage spells), it will replace said spells with MP draining spells if the target has MP, even if these are so ineffective as to COST more MP then they gain. And it will do this until it either gets above 75% MP or it runs out of MP. If it gets damaged in the process, it will alternate HP draining spells with MP draining spells, which are equally ineffective as they share the same resistance mechanism.
Dynasty Warriors Online. Hoo boy. For the standard mooks, it's no surprise the A.I. isn't all that good. For computer controlled player characters, it almost becomes insulting. Here's a quick laundry list of why they're no good as enemies or allies:
1.) They have their priorities massively skewed. They always target bases only. Always. Even if it's the wrong game mode, they, like a baseball player, head straight to base.
2.) They don't attack or block nearly often enough. Where a player would be blocking an attack or taking advantage of an opening, A.I. will just watch you. Don't be fooled by the blocking stance they take, when moving blocking doesn't work, they just use it so they face you. Also, in an inversion of Secret A.I. Moves, there are some moves they just can't seem to grasp using.
3.) They are directionless and cannot be commanded. You may wonder "If they aren't that good, why would you want to command them?" Well, because their priority means they attack bases, and there are game mode when that is how you win. But, if you go into a base they are trying to capture you can't lead them anywhere without using enemy mooks so they chase after you. If not, then they will not move at all until they find an enemy to chase the base is captured and they go after a new one. Depending on the base type you may not have to worry about directing them, or you may get annoyed because it would be really nice to have their help attacking a tower.
And, finally, the strongest enemy type you will face, musou generals who are the original characters from dynasty warriors, have this exact same A.I. On one hand they can take you out with about 3 swings unless you're a tank. On the other hand, they have the same restrictions as above and thus are just as dumb as stated above. Were not for the Instant Death Radius they have they would be considered a joke.
In Neverwinter Nights 2, if the A.I. is turned on, your character will always, always start the combat by casting the Sanctuary spell. Even if he is a warrior/cleric.
There is also Qara, who had a habit of aiming area-of-effect spells where they would hurt fellow party members and even herself. While she isn't portrayed as very bright, she shouldn't be that stupid.
Let's not forget how your spellcasters would always sling about the various dispelling spells they had prepared at the beginning of a fight. Most of the time this led to you not having a way of getting rid of an enemies buff spells half way through a fight because they'd all already been used.
Even worse, they would often dispel any buff spells on the PCs, making it easier for the enemies to kill you.
Thankfully, you have the option to customize what kinds of spells your party members use, how often they use Ao E spells, and even turn off the option of spells affecting your own party.
Linu back in the original Neverwinter Nights had an unfortunate habit of casting Harm on hostile undead. Which HEALS them. Even worse, this was usually a few rounds into the battle, so it'd wipe out all the damage you'd painstakingly inflicted on it. Throw in her tendency towards burning through her whole day's supply of Turn Undead spells, even though the last three attempts did nothing... yeah, it's probably best to depend upon potions for your healing.
The non-mages aren't a whole lot better. Fighter-types running headlong into encounter after encounter, thus forcing you to abandon what you were doing to join in, makes some amount of sense. However, Neeshka does exactly the same thing even though the sensible thing to do would be to wait until others engage and then sneak attack (where it works) at will (there is unfortunately no option to set up a character to only use sneak attacks. The best you can hope for is to tell her to remain in the shadows).
Of course when the fighters attack, they have a nasty tendency to run past perfectly viable targets, and get attack of opportunity-ed, just so they could get to that oh so dangerous archer that shot them in the bum. "Oh you'll pay for that 4 damage bow boy! What? Oh that huge-assed guy that just power attacked me for 36? Nah he's no threat, I won't bother to change my priorities just because he can dish out nine times the damage, that's sissy thinking!"
Anyone remember the very useless sorcerer Boddyknock? Casting See Invisibility (repeatedly!) on clearly visible enemies wasn't of any help at all, while you were in dire need of support.
He also has the annoying tenancy to cast invisibility spells on himself during combat and leave to to fend for yourself.
Follower casters also routinely get caught behind corners and other obstacles where they can't see the opponent, cast a spell at the unseen enemy (which they only know is there because they can hear it), then immediately lose the spell because they can't target someone they can't see properly. Then repeat over and over, wasting their spells and time while you have to deal with the enemies on your own.
None of the NPCs seem to realize that traps are dangerous things to be avoided. Neeskha will happily start disarming a trap, spot an enemy, and run straight over the trap to attack it.
Due to game engine specs, buffs vanish when moving to a new area, even though you're leaving the tavern through the door and those buffs should last for minutes or even hours. There's more than one scripted event where you get ambushed outside the tavern, too. The protagonist will also happily walk into scripted events and conversations that very obviously will or could turn hostile without any chance to buff, prepare or attack first.