Looks to me like there are two different kinds of bad protagonist; the annoying and the unconvincing. As far as annoyance goes, I've never found one worse than Tidus from FF10. Love the game, but it would be substantially improved if the first thing Auron did at the start of the game was gag Tidus...
Unconvincing-wise, I'm tempted to start laying the hate on AFGNCAAPs (I'm looking at you, Mr. Freeman, even if you aren't technically faceless, nameless or gender-neutral), because playing through a whole game without my character having any motivation other than 'someone I've only just met told me to' is a bit unconvincing.
HOWEVER, there is a stratum below AFGNCAAPs, which is characters that the writer tried to make seem heroic and noble but who actually come off as naive idiots, like Vyse from my favourite punching bag, Skies of Arcadia. This is a guy who forgives anyone who attacks him, no matter how misguided or selfish their reasons. What's worse is that everyone he defeats undergoes some sort of bizarre conversion from callous thief/murderer/rapist/kidnapper to goody-two-shoes instantly, the moment he's nice the them. Convincing? I think not.
Oh, and then there's the moment where he arrives at his childhood best friend's prison cell to discover an enemy commander in the process of sexually assaulting her and before he attacks the man, pauses to make a wisecrack about how maybe she'd like to be left alone with him. That made my skin crawl.
So, overall, Vyse is the worst character I can remember playing as.