Like you say, all franchise stories turn to shit given enough instalments, so the question is redundant. It'd either be none or a list of "franchises" with very few instalments.
Really the question should be something like: "Which gaming franchise has had the biggest drop in writing quality?"
Of course that brings a whole bunch of new issues with it. Is it from one specific game to the next in the franchise? Is it overall from the first to the latest? What about stuff like Silent Hill or Legacy of Kain that has peaks and valleys? And so on.
Also, regardless of what the question is, do spin-offs count?
The idea of the poll is actually to pinpoint the worst offenders and examples of how story/writing turned to shit in a frahnchise. I'm sorry if the title is badly worded. (That's why you only get 6 votes)
Also, spin-offs count within the franchise