I was going to ask whether escort missions should disappear from the face of the earth or something along those lines, maybe throw a poll to boot, but after some consideration, not all of them are bad and some can make pretty awesome games on their own! Case in point:
So instead let's make this about the WORST escort mission you've played through, and throw in a pic for fun. This guy from Spyro 2 inscribed itself in my childhood as my eternal woe:
EDIT - Welp I rounded up the games mentioned and this is what I came up with:
5 votes against: Dead Rising (assorted), GoldenEye (Natalya), Spyro 2: Rypto's Revenge (The Alchemist) and World of Warcraft (assorted).
4 votes against: Dead Island (assorted), Dragon's Dogma (assorted) and Metal Gear Solid 2 (Emma Emmerich).
3 votes against: Bioshock (Little Sisters), Fable (The Architect), Resident Evil 4 (Ashley... really?) and Morrowins (assorted).
2 votes against: Amy (Amy), Mass Effect 3 (assorted), Oblivion (assorted), Resident Evil 5 (Sheva) and The Witcher (assorted).
Etc. Keep 'em coming!

So instead let's make this about the WORST escort mission you've played through, and throw in a pic for fun. This guy from Spyro 2 inscribed itself in my childhood as my eternal woe:

EDIT - Welp I rounded up the games mentioned and this is what I came up with:
5 votes against: Dead Rising (assorted), GoldenEye (Natalya), Spyro 2: Rypto's Revenge (The Alchemist) and World of Warcraft (assorted).
4 votes against: Dead Island (assorted), Dragon's Dogma (assorted) and Metal Gear Solid 2 (Emma Emmerich).
3 votes against: Bioshock (Little Sisters), Fable (The Architect), Resident Evil 4 (Ashley... really?) and Morrowins (assorted).
2 votes against: Amy (Amy), Mass Effect 3 (assorted), Oblivion (assorted), Resident Evil 5 (Sheva) and The Witcher (assorted).
Etc. Keep 'em coming!