Usually... it depends. Most games will have a handful of shaders that are used for most of the games content. Then there will be a crap ton of specific shaders for special objects.
I think there will be different shader scripts for specialized things... like showing that a character currently has a power up or something.
But normally shaders will find themselves often getting reused, and by design the programmable pipeline is meant for reuse.
Now that's not saying that there aren't objects that get their own specialized shaders. There will be times when an object needs an appearance created analytically, or programmatically.
For example... say that you have an object with glowy lines over it's surface. And you want a bright halo to run down the lines over time. You'll need a special shader for that object.
For Uber Shaders... it tends to be a big pain in the ass to use it for every visual effect in the game, unless the appearance won't vary all that much. The uber shader would probably shine best when it comes to some common features about a material.