Well, i place some value on the story of a game and i am disappointed quite fast, if it has some major flaws.
One example was Fallout 3.
The intro in the Vault was great until to the point, when i have found out that my father had left me back, because he wanted to help some strangers at the outside. Great i will grow old an die in this bunker.
But as loyal child i have decided to flee and to find him (i have no clue why, he has left me behind.)
After serveral months (and a lot of side quests) i still ask barkeepers "Have you recently seen on older man?" and finally i have found him and i still don´t no why i was looking for him.
Anyway, a quick jump to the ending, which was horrible as well.
We have killed the bad guys, but we had to stop the machine or a lot of innocents will die. The problem, the controll room was already contaminated and when we try to stop the process, one of us will die.
Haa, no problem since i have a mutant as companion, who is immune to nuclear radiation, he could press the buttons and none has to die.
And then he told me "It is your fate to die here, i will not help you." Great. Luckily there was another companion. (The whole thing was fixed by a dlc, and then you could survive the ending.)
The Fallout: New Veags was a way better storywise. Someone wants to kill you, you survive and track them down and find some leads to a conspiracy. This has worked great for me.
Bioshock was a bit different.
I have really liked Systemshock and have hoped that Bioshock will be something similar with a different setting and some improvements.
In the end i have got a different setting but the rest was a dumbed-down copy of Systemshock with less features.
Bioshock:Infinite on the other hand was much better. Sure, it is even more a simple shooter as Bioshock, but it has a quite interesting story and it does not try to be a Systemshock.