According to Wikipedia, there have been 27 Resident Evil games so far. As far as I can tell, the plot of all of them is "The Umbrella Corporation makes zombies and you kill them." (In this game the remains of Umbrella is hiding behind another company, but it's still the same thing.)
About five hours into Resident Evil 5 - five hours of shooting zombies - you come upon a crate with the Umbrella Corporation logo and Chris Redfield says in surprise, "Umbrella Corporation! What are they doing here?" This made me giggle. When we have a zombie problem, shouldn't we just assume this is an Umbrella thing until proven otherwise?
I think the series is stuck in a rut, plot wise. Actually, I guess the story was constructed in a rut and has simply stayed there. I was never crazy about how the dramatic focus is always on the Umbrella employees and not the monsters. The game is strongest when it's focusing on the freak show of foes, and turns into a farce whenever the fighting stops so you can chat with some silly-suited goof from Umbrella Corporate headquarters. It's like if someone kept inserting clips of The Office into the middle of Aliens.
The story has taken this one very bland idea and stretched it impossibly thin, repeating the same theme while adding layer after layer onto the nonsense. In the end the main villain comes off as simply being Too Stupid To Stay in Business, which isn't exactly a good way to ramp up the tension in your narrative.
There are rumors that Resident Evil 6 might be a reboot of the franchise. Normally this is a good option if your franchise has gotten so tangled up in its own backstory that it's infuriating to fans and incomprehensible to newcomers. But I have this suspicion that if Capcom did reboot things, they would turn right around and tangle it up again, simply replacing the old mess with a new one.
What would you do with the Resident Evil story if Capcom asked you to handle the reboot?