Late in the original BioShock, you're tasked with escorting a Little Sister, which wouldn't be so bad normally, given they're invincible ADAM factories. Unfortunately, this Little Sister isn't like the ones earlier in the game - she's now able to be killed, yet still insists on stopping to harvest ADAM along the way. But what makes this Little Sister truly irritating is that she keeps saying the same dumb quotes over and over ("Come on, Mr. B! Time to find some angels!"), seemingly oblivious to the fact that you're blasting away at an army of splicers there to kill the both of you. Would it kill her to show some appreciation for the fact that you're protecting her from the onslaught of psychopaths? At least stop telling you to hurry when you're 20 feet in front of her and she's crouched down, jamming a needle into a corpse.
The Meat Circus (combining Raz's childhood circus memories and Oly's memories of his father's butchershop) is something of a perfect storm for terrible escort missions: Oly's entirely defenseless against enemies (as you try to catch up with him to protect him while his health meter shrinks), he's constantly running (well, waddling) away from you, and his high-pitched wailing is annoying as hell (YES, OLY, I KNOW SOMETHING IS HURTING YOU, THAT'S WHY YOU SHOULD STAY NEAR ME INSTEAD OF FLYING TOWARDS MEAT PLATFORMS TO GRAB BUNNIES). The only thing more annoying than Oly himself is the level he's found himself in - the Meat Circus is nearly impossible to navigate, thanks to some truly unforgiving platforming along with some iffy controls. The whole thing ends up accidentally providing a pretty solid argument for vegetarianism.
Escorting an actual baby is never a good start for any type of escort mission game, especially one who screeches whenever he's not riding you ("you" being a dinosaur that eats everything it possibly can, which should justifiably TERRIFY the baby, but doesn't because the baby is too stupid to realize how horrible its life is). Really, the game is very fun in spite of this central escort dynamic, and Baby Mario isn't too awful, since he pretty much just sits on you the entire game. What makes him awful is that crying/screeching as he floats away in a bubble whenever he gets separated from you. If only you were an actual dinosaur, you would just eat him and be done with it. And given his parents thought an okay way for him to travel was in the beak of an incompetent stork, you'd probably be doing him a favor.