Any member of the generic elite team in an Action or First Person Shooter, other than the character the player controls. Because death is just around the corner for these characters. And usually pretty early during some generic disaster that wipes out the entire team except for the main character who must soldier on. Sure, they get a free helicopter, boat, submarine or time machine ride to some exotic location, but what's the fun when they're soon to be shot, blown up, torn to pieces or just go missing, so I would rather pass.
Any Tier 1 unit in any strategy game. Fodder. Early game, sure there's some glory, but by the end of those games the Tier 1 units are usually for fodder, diversion attacks that no one is coming back from, or to sit around in random defensive spots until other more important units either win the game, or you're overrun and they're slaughtered. Creatures that outlive their usefulness and are relegated to suicidal attacks or babysitting unimportant locations, I'm sure it must be fun guarding a corner of a map for the entirety of your life, but count me out.
The escortee in any Escort Mission. Despite being the target of whatever malevolent forces are at work, most of these characters suffer from severe mental and/or physical disabilities. Running into walls, getting stuck on barrels, getting lost, running in front of people shooting are all par for the course for these poor handicapped souls, being among their ranks is not high on my list of dreams.