Mocks/stubs/fakes/test doubles/etc. are fine in unit tests, and permit testing the class/system under test in isolation. Integration tests might not use any mocks; they actually hit the database or other external dependency.
You use a mock or a stub when you have to. Generally this is because the class you're trying to test has a dependency on an interface. For TDD you want to program to interfaces, not implementations, and use dependency injection (generally speaking).
A very simple case:
public class ClassToTest
{
public ClassToTest(IDependency dependency)
{
_dependency = dependency;
}
public bool MethodToTest()
{
return _dependency.DoSomething();
}
}
IDependency is an interface, possibly one with expensive calls (database access, web service calls, etc.). A test method might contain code similar to:
// Arrange
var mock = new Mock<IDependency>();
mock.Setup(x => x.DoSomething()).Returns(true);
var systemUnderTest = new ClassToTest(mock.Object);
// Act
bool result = systemUnderTest.MethodToTest();
// Assert
Assert.That(result, Is.True);
Note that I'm doing state testing (as @Finglas suggested), and I'm only asserting against the system under test (the instance of the class I'm testing). I might check property values (state) or the return value of a method, as this case shows.
I recommend reading The Art of Unit Testing, especially if you're using .NET.