Don't think I could narrow it down to to one. Lot of games have lousy storylines, and plenty of those love to beat you over the head with it.
Top of my head Fear Effect had a really lousy story about demons and crap that rambled on and didn't make any sense untill the last disc, at which point I long stopped caring. I rescue someone's daughter from terriosts, then I'm in a village of zombies, then a whore house full of she-demons, then hell. Sadly the gameplay is so lousy the cutscenes were still the rewarding parts.
Also Perfect Dark, despite being a good game, had a really awful story as well, and it changed far too often as well. First you need to save Dr. Carol from DataDyne, then Carrington who apprently thought it was smart to take Dr. Carol somewhere that's easily ambushed, go spy on DataDnye's people, off to Area 51 to resuce an alien, then sneak on Air Force One to warn the president about a conspiracy, Air Force One crashes, kill the President's clone, go reclaim a sub-bay, find Dr. Carol in a giant alien (Different then the first two sets of aliens) ship underwater, blow the place up, get honored, get captured, go to Skedar homeworld, murder their grand high jackass warlord. Yeesh.
