I can stand a bit of shaky-cam. It doesn't really affect my stomach. But, depending on how it's done, it can be just annoying.
For example, in Cloverfield, you have the person holding the camera at an angle. Who does that? Maybe a slight angle, but not a 45-degree one. At one point in a subway station, he sets the camera down to keep on filming. Most cameras have some sort of rectangular shape. You'd either set it down on the bottom and have a normal picture or it might roll sideways and be tilted 90 degrees. But 45 degrees again? You'd have to purposely prop it up like that.
A little bit of shake for realism is OK. But to purposefully exagerate bad camera handling really annoys me. We get the point. It's hand-held amatuer footage. Why be annoying with it too?
What's even more annoying is the assumption that these people film everything. At what point do you drop the camera and run? Or put it away? Or even throw it at the thing chasing you?
I hear they're planning a Cloverfield 2. Another person in the city with a camera too. Doing the same thing as #1, but from different locations.
What's wrong with just telling the same story with traditional steady camera shots? Why does it have to be amatuer film? I think the story could have been OK without it. It's the story of survival in a siege situation and not your sterotypical giant monster movie where the army comes in and blasts it away. It's still a good character study and still has action and suspense.