Exactly those classes which are necessary to understand the aspect of the system which that particular class diagram depicts.

It could be the entire domain model, or all classes that make up the external API of a particular layer or subsystem, or whatever you think is important.

But note that class diagrams are not the only type of diagram, nor the most useful one.

First of all, you are not limited to one class diagram. You can have as many diagrams as you want! the purpose of the class diagrams is to help you (or someone else) understand the system better, so it is mostly a problem of taste. Some people need to see all of the details to understand the structure of the system and so they need one big class diagram. But other people prefer having the big picture separated into smaller chunks where each one shows only a part of the system, and they can build their own “big picture” in the head.

BTW, you can also create a component diagram that connects the small details of the class diagrams into a more high-level diagram.

You should include all classes in your program, as a class diagram is suppose to describe the entire structure of your program/application.

However, in many applications this process could turn quite complex, so try to isolate the main components (Data Access Layer, Service Layer, Business Layer, etc.) and graph them independently, with proper documentation as to how they interact with each other.

For the class diagram to be useful, you need to divided it by layers, and by components within these layers, if necessary. If it is still too complex, it means you might need to rethink the relationships among your classes. Mapping them all out can help you understand which ones are needed, which ones can be combined, or which deleted, and improve it to the point you have a simpler class diagram, thus a simpler program structure.

I try to include every class, but sometimes during implementation I may find that a class is rather big, so I split it into small helper classes. I typically don’t bother putting them into the class diagram because it would offer little value. They are not design artifacts.

But start off by including everything in your diagram.

A class diagram represents an individual component of a system, or the system as a whole. At the highest level you have a System context diagram which shows the individual components of a system.

Class diagrams could represent all classes in a small project however you would be far better placed to have multiple diagrams representing each component in your project.