Dependency injection through constructors or property setters?

The users of a class are supposed to know about the dependencies of a given class. If I had a class that, for example, connected to a database, and didn't provide a means to inject a persistence layer dependency, a user would never know that a connection to the database would have to be available. However, if I alter the constructor I let the users know that there is a dependency on the persistence layer.

Also, to prevent yourself from having to alter every use of the old constructor, simply apply constructor chaining as a temporary bridge between the old and new constructor.

public class ClassExample
{
    public ClassExample(IDependencyOne dependencyOne, IDependencyTwo dependencyTwo)
        : this (dependnecyOne, dependencyTwo, new DependnecyThreeConcreteImpl())
    { }

    public ClassExample(IDependencyOne dependencyOne, IDependencyTwo dependencyTwo, IDependencyThree dependencyThree)
    {
        // Set the properties here.
    }
}

One of the points of dependency injection is to reveal what dependencies the class has. If the class has too many dependencies, then it may be time for some refactoring to take place: Does every method of the class use all the dependencies? If not, then that's a good starting point to see where the class could be split up.

Well, it depends :-).

If the class cannot do its job without the dependency, then add it to the constructor. The class needs the new dependency, so you want your change to break things. Also, creating a class that is not fully initialized ("two-step construction") is an anti-pattern (IMHO).

If the class can work without the dependency, a setter is fine.