I join all three of you. It's the worst story in any Sonic game. 

Metal Gear Solid IV. Convoluted, terrible, and if you can't explain something "nanomachines!". It like Kojima thought nanomachines was synonym for plot hole remover.

All that said, still better than FFVII's plot. A tale of identity theft, domestic violence, sudden unprovoked homicidal rage, and evil for no reason. I'm looking at you Hojo. Also it managed to take a series staple, Ninja, and ruin it. Yuffie. You suck.

Zero Escape maybe?

Toss up between the Kingdom Hearts series and Sonic '06.

The one that immediately comes to mind for me is Final Fantasy VIII. To be honest it was so confusing that I don't really remember it, I just recall some nonsense about every character having grown up together but they forgot due to some collective amnesia though it seemed they'd all gathered purely by chance... They wound up in space at some point as well...

It could be that I was just young and the translation wasn't great, but I had no problem following vi, VII, ix, or x, and VII was pretty darn confusing itself. I just couldn't make heads or tails of it.

Oh, also that CoD modern warfare trilogy. I think I only played through the second one, but I had to roll my eyes when the Russians were suddenly parachuting into suburban America. Almost as believable as North Korea becoming a global superpower.

I'm not defending COD here but, do you only play games that are "believable"? 

This I have to give it to Metal Gear Solid 2. It took me quite many playthroughs to fully grasp and understand what Kojima was going for on this game.

For me, the Metal Gear franchise. Good lord!

Shadow of Destiny. Watch Retsupurae's Longplay of it to see just how crazy the plot is.